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Convex and balanced set
subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead
Absolutely_convex_set
In geometry, set whose intersection with every line is a single line segment
closed convex subset is strictly convex if and only if every one of its boundary points is an extreme point. A set C is absolutely convex if it is convex and
Convex_set
Property of point sets in Euclidean spaces
transformation of A {\displaystyle A} . Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point
Star_domain
Length in a vector space
1\right\}.} Conversely: Any locally convex topological vector space has a local basis consisting of absolutely convex sets. A common method to construct such
Norm_(mathematics)
Space with topology generated by convex sets
locally convex space or LCTVS. In fact, every locally convex TVS has a neighborhood basis of the origin consisting of absolutely convex sets (that is
Locally convex topological vector space
Locally_convex_topological_vector_space
Set that can be "inflated" to reach any point
D:={\textstyle \bigcap \limits _{|u|=1}}uW} will be convex and balanced (also known as an absolutely convex set or a disk) in addition to being absorbing in
Absorbing_set
Topics referred to by the same term
drive Disk (mathematics), the region in a plane bounded by a circle Absolutely convex set of a real or complex vector space Intervertebral disc, a cartilage
Disc
Property of group subsets (mathematics)
symmetric sets. Any balanced subset of a real or complex vector space is symmetric. Absolutely convex set – Convex and balanced set Absorbing set – Set that
Symmetric_set
Haar null set Convex set Balanced set, Absolutely convex set Fractal set Recursive set Recursively enumerable set Arithmetical set Diophantine set Hyperarithmetical
List_of_types_of_sets
Construct in functional analysis
sublinear function. Absolutely convex set – Convex and balanced set Absorbing set – Set that can be "inflated" to reach any point Bounded set (topological vector
Balanced_set
Generalization of boundedness
vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von
Bounded set (topological vector space)
Bounded_set_(topological_vector_space)
Function made from a set
{\textstyle K} is convex then p K {\textstyle p_{K}} is subadditive. If K {\textstyle K} is balanced then p K {\textstyle p_{K}} is absolutely homogeneous;
Minkowski_functional
Theorem in optimal transport
that the optimal transportation plan of an absolutely continuous probability measure is the gradient of a convex function. More precisely, if μ {\displaystyle
Brenier's_theorem
In mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Mathematical function for the probability a given outcome occurs in an experiment
an absolutely continuous and a singular continuous distribution, and thus any cumulative distribution function admits a decomposition as the convex sum
Probability_distribution
Vector space with a notion of nearness
countable dimension then every string contains an absolutely convex string. Summative sequences of sets have the particularly nice property that they define
Topological_vector_space
Mode of convergence of an infinite series
mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands
Absolute_convergence
Concept in financial economics
instead of the sublinear property,R is convex, then R is a set-valued convex risk measure. A lower semi-continuous convex risk measure ϱ {\displaystyle \varrho
Coherent_risk_measure
Strong form of uniform continuity
continuous ⊂ absolutely continuous ⊂ uniformly continuous ⊂ continuous. Given two metric spaces (X, dX) and (Y, dY), where dX denotes the metric on the set X and
Lipschitz_continuity
Order-preserving mathematical function
monotonicity in a set of data Total monotonicity Cyclical monotonicity Operator monotone function Monotone set function Absolutely and completely monotonic
Monotonic_function
Complement of an open subset
somewhere. In convex analysis, closedness is commonly expressed through epigraphs. A convex function is called closed when its epigraph is a closed set. This
Closed_set
Problem optimization method
thought, let's kill two birds with one stone. Let's take a word that has an absolutely precise meaning, namely dynamic, in the classical physical sense. It also
Dynamic_programming
Infinite sum of monomials
region, is a convex set. More generally, one can show that when c=0, the interior of the region of absolute convergence is always a log-convex set in this
Power_series
Mathematics concept
monotonicity. Gradients of convex functions are cyclically monotone. In fact, the converse is true. Suppose U {\displaystyle U} is convex and f : U ⇉ R n {\displaystyle
Cyclical_monotonicity
Theorem in mathematics and economics
first-order condition for (1), which requires that the choice set X {\displaystyle X} have the convex and topological structure, and the objective function f
Envelope_theorem
Concept in mathematics
4064/fm-20-1-262-176 Bourgin, Richard D. (1983). Geometric Aspects of Convex Sets with the Radon-Nikodým Property. Lecture Notes in Mathematics 993. Vol
Bochner_integral
Type of random variable ordering
of stochastic orders.[citation needed] Convex order is a special kind of variability order. Under the convex ordering, A {\displaystyle A} is less than
Stochastic_ordering
Function spaces generalizing finite-dimensional p norm spaces
is not locally convex: in ℓ p {\displaystyle \ell ^{p}} or L p ( [ 0 , 1 ] ) , {\displaystyle L^{p}([0,1]),} every open convex set containing the 0
Lp_space
Type of function in linear algebra
function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known
Sublinear_function
Mathematical function
connected with convex sets: every seminorm is the Minkowski functional of some absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm
Seminorm
mathematics, a convex measure is a probability measure that — loosely put — does not assign more mass to any intermediate set "between" two measurable sets A and
Convex_measure
1983 film by David Cronenberg
Barry Convex, with his crew operating a dummy underneath the set. Lennick devised effects such as having the image of the Videodrome television set distort
Videodrome
multiplication means that for every absolutely convex neighborhood V {\displaystyle V} of zero, there is an absolutely convex neighborhood U {\displaystyle
Fréchet_algebra
Topological vector space
described by specifying that an absolutely convex subset U of X is a neighborhood of 0 if and only if U ∩ Xi is an absolutely convex neighborhood of 0 in Xi for
LF-space
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
ℓ 1 {\displaystyle \ell ^{1}} of absolutely convergent series. Let X {\displaystyle X} be a Hausdorff locally convex space. Then the following are equivalent:
Nuclear_space
Statistical value representing the center or average of a distribution
ranked relative to each other but are not measured absolutely. Mode the most frequent value in the data set. This is the only central tendency measure that
Central_tendency
Probability problem
corresponding to the same prescribed moments and they consist of a convex set. The set of polynomials may or may not be dense in the associated Hilbert
Hausdorff_moment_problem
Objects that generalize functions
collection of convex balanced subsets W of X such that W ∩ Xi is open for all i. A base for the inductive limit topology τ then consists of the sets of the form
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Normed vector space that is complete
locally convex because the set of all open balls centered at the origin forms a neighbourhood basis at the origin consisting of convex balanced open sets. This
Banach_space
Function with a multiplicative scaling behaviour
\infty ]=\mathbb {R} \cup \{\pm \infty \},} which appear in fields like convex analysis, the multiplication 0 ⋅ f ( x ) {\displaystyle 0\cdot f(x)} will
Homogeneous_function
Integral expressing the amount of overlap of one function as it is shifted over another
distributions are μ and ν. In convex analysis, the infimal convolution of proper (not identically + ∞ {\displaystyle +\infty } ) convex functions f 1 , … , f
Convolution
Type of vector space in math
things named after David Hilbert Locally convex topological vector space – Space with topology generated by convex sets Operator topologies – Topologies on
Hilbert_space
Variable representing a random phenomenon
an absolutely continuous part; see Lebesgue's decomposition theorem § Refinement. The discrete part is concentrated on a countable set, but this set may
Random_variable
Type of topological vector space
Bourbaki (1950). A convex and balanced subset of a real or complex vector space is called a disk and it is said to be disked, absolutely convex, or convex balanced
Barrelled_space
is the Mackey topology, the topology of uniform convergence on all absolutely convex weakly compact subsets of X ′ {\displaystyle X'} . Given a dual pair
Dual_topology
Fundamental theorem in probability theory and statistics
mean and same covariance matrix as S {\displaystyle S} . Then for all convex sets U ⊆ R d {\displaystyle U\subseteq \mathbb {R} ^{d}} , | P [ S ∈ U ] −
Central_limit_theorem
Middle quantile of a data set or probability distribution
interval (allowing the degenerate cases of a single point or an empty set). Every convex function is a C function, but the reverse does not hold. If f is a
Median
Mathematical object
polytope. For the following definitions. Let K be a bounded convex set in a Euclidean space: The convex hull of random points selected with respect to a uniform
Random_polytope
Barrelled space where closed and bounded subsets are compact
function X → c 0 {\displaystyle X\to c_{0}} sends closed bounded absolutely convex subsets of X {\displaystyle X} to relatively compact subsets of c
Montel_space
Topological vector space whose topology can be defined by a metric
LM-space is an inductive limit of a sequence of locally convex metrizable TVS. A pseudometric on a set X {\displaystyle X} is a map d : X × X → R {\displaystyle
Metrizable topological vector space
Metrizable_topological_vector_space
Generalized notion of measure in mathematics
\ldots ,A_{n},\ldots } of disjoint sets in Σ . {\displaystyle \Sigma .} The series on the right must converge absolutely when the value of the left-hand
Signed_measure
Infinite sum
addition. Together with series addition, series multiplication gives the sets of absolutely convergent series of real numbers or complex numbers the structure
Series_(mathematics)
locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely, given locally convex topological
Projective_tensor_product
asymptotically almost surely. AC – Axiom of Choice, or set of absolutely continuous functions. a.c. – absolutely continuous. acrd – inverse chord function. ad
List of mathematical abbreviations
List_of_mathematical_abbreviations
Function that measures dissimilarity between two probability distributions
absolutely continuous with respect to Q {\displaystyle Q} (meaning Q > 0 {\displaystyle Q>0} wherever P > 0 {\displaystyle P>0} ). Then, for a convex
F-divergence
German mathematician (1945–2018)
German mathematician known for his contributions to integral geometry, convex geometry, and stochastic geometry. He was a professor of mathematics at
Wolfgang_Weil_(mathematician)
constraint set the underlying equilibrium problem was working on, e.g. nonnegativity of investments in financial modeling, convex polyhedral sets in operations
Projected_dynamical_system
Theorem in functional analysis
vector e n ∈ V {\displaystyle e_{n}\in V} . Because the set of norm-1 points make up a convex symmetric body in V {\displaystyle V} , there exists a hyperplane
Auerbach's_lemma
Property of a mathematical space
The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the
Dimension
Banach space as a closed subset of the convex hull of the image. Fσ set An Fσ set is a countable union of closed sets. Filter See also: Filters in topology
Glossary_of_general_topology
Grothendieck trace theorem. More generally, an operator from a locally convex topological vector space A {\displaystyle A} to a Banach space B {\displaystyle
Nuclear operators between Banach spaces
Nuclear_operators_between_Banach_spaces
Mathematical model of the physical space
complete sets of axioms. To the ancients, the parallel postulate seemed less obvious than the others. They aspired to create a system of absolutely certain
Euclidean_geometry
Theorem in Optimal Transport
\Omega } is a convex subset of R d {\displaystyle R^{d}} , and μ {\displaystyle \mu } a measure on Ω {\displaystyle \Omega } which is absolutely continuous
Polar_factorization_theorem
Average value of a random variable
any Borel set A {\displaystyle A} , in which the integral is Lebesgue. the cumulative distribution function of A {\displaystyle A} is absolutely continuous
Expected_value
topology on X {\displaystyle X} can be described by specifying that an absolutely convex subset U {\displaystyle U} is a neighborhood of 0 {\displaystyle 0}
LB-space
Extension of the factorial function
positive reals, which is logarithmically convex, meaning that y = log f ( x ) {\displaystyle y=\log f(x)} is convex. The notation Γ ( z ) {\displaystyle
Gamma_function
Concept in information theory
. The set of entropic vectors is denoted Γ n ∗ {\displaystyle \Gamma _{n}^{*}} , following the notation of Yeung. It is not closed nor convex for n ≥
Inequalities in information theory
Inequalities_in_information_theory
Average uncertainty in variable's states
1} . Accordingly, the negative entropy (negentropy) function is convex, and its convex conjugate is LogSumExp. The inspiration for adopting the word entropy
Entropy_(information_theory)
Mathematical statistics distance measure
Relative entropy D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} is convex in the pair of probability measures ( P , Q ) {\displaystyle (P,Q)} , i
Kullback–Leibler_divergence
Polish mathematician (1910–1943)
worked mainly on Functional analysis. On the basis of his 1936 paper on convex sets in linear normed spaces, geometric versions of the hyperplane separation
Meier_Eidelheit
Mathematical concept
function G {\displaystyle G} can be chosen to be monotone increasing and convex. Uniform integrability gives a characterization of weak compactness in L
Uniform_integrability
Generalized function whose value is zero everywhere except at zero
finite Radon measures on X, equipped with its vague topology. Moreover, the convex hull of the image of X under this embedding is dense in the space of probability
Dirac_delta_function
Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. For a twice differentiable
Glossary_of_calculus
Business philosophy
shareholders. Packard, who was in attendance, stood up and said: "I think you’re absolutely wrong. Management has a responsibility to its employees, it has a responsibility
The_HP_Way
Field of knowledge
geometry, the study of finite configurations in geometry. Convex geometry, the study of convex sets, which takes its importance from its applications in optimization
Mathematics
Risk measure estimating the average loss in the worst tail of the distribution
α {\displaystyle {\mathcal {Q}}_{\alpha }} is the set of probability measures which are absolutely continuous to the physical measure P {\displaystyle
Expected_shortfall
Mathematical space with a notion of distance
another metric space which can be thought of as an abstract version of the convex hull. The knight's move metric, the minimal number of knight's moves to
Metric_space
{\displaystyle V} is a normed space or (more generally) is a Hausdorff locally convex TVS. Evaluation of a functional may be written as a duality pairing: ⟨ φ
Pettis_integral
Theory of perception
tend to perceive as figures those parts of our perceptual fields that are convex, symmetric, small, and enclosed. Gestalt psychology contributed to the scientific
Gestalt_psychology
{\displaystyle C} ). The set of injections E B → E {\displaystyle E_{B}\to E} where B {\displaystyle B} runs through all bounded absolutely convex subsets in E
Convenient_vector_space
Probability distribution
reverse J-shaped with a right tail, positively skewed, strictly decreasing, convex mode = 0 0 < median < 1/2. 0 < var ( X ) < − 11 + 5 5 2 , {\displaystyle
Beta_distribution
Family of probability distributions related to the normal distribution
opposite order, for the convex conjugate function. Fixing an exponential family with log-normalizer A {\displaystyle A} (with convex conjugate A ∗ {\displaystyle
Exponential_family
British mathematician (1920–2005)
numbers, Hausdorff measures, analytic sets, geometry of Banach spaces, selection theorems and finite-dimensional convex geometry. In the theory of Banach
Claude_Ambrose_Rogers
Fourier transform of the probability density function
is convex for t > 0 {\displaystyle t>0} , φ ( ∞ ) = 0 {\displaystyle \varphi (\infty )=0} , then φ(t) is the characteristic function of an absolutely continuous
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Italian author and blackmailer (1492–1556)
one time, Aretino owned the painting by Parmigianino, Self-Portrait in a Convex Mirror. Aretino is said to have died of suffocation from "laughing too much"
Pietro_Aretino
Structure in functional analysis
definition consists of all equicontinuous weak-* closed and weak-* bounded absolutely convex subsets of X ′ {\displaystyle X^{\prime }} (which are necessarily
Complete topological vector space
Complete_topological_vector_space
Number divisible only by 1 and itself
empty) set of distinct Pierpont primes, primes of the form 2 a 3 b + 1 {\displaystyle 2^{a}3^{b}+1} . It is possible to partition any convex polygon
Prime_number
Computation machine that uses continuously varying data technology
model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the convex hull of a set of points; and strings tied together
Analog_computer
Theorem in mathematics
theorem is stated such: Let f : Ω → C be a holomorphic function on the open convex set Ω, and let a and b be distinct points in Ω. Then there exist points u
Mean_value_theorem
Genus of theropod dinosaurs
suggesting that it was a pursuit predator, and had forelimbs which were both absolutely and proportionally larger than its relatives. Nanotyrannus is the only
Nanotyrannus
Numerical method for solving physical or engineering problems
order p method. Under specific hypotheses (for instance, if the domain is convex), a piecewise polynomial of order d {\displaystyle d} method will have an
Finite_element_method
Measure that has a notion of derivative
usually one chooses X {\displaystyle X} to be a real Hausdorff locally convex space with the Borel or cylindrical σ-algebra A {\displaystyle {\mathcal
Differentiable_measure
Observed inability to reproduce scientific studies
(its "traits"). A lab might use more "effort", making the ROC curve more convex but decreasing productivity. A lab accumulates a score over its lifetime
Replication_crisis
Technology for creating optical illusions
critical registration of the fine "slices" of interlaced images must be absolutely correct during the lithographic or screen printing process to avoid "ghosting"
Lenticular_printing
History of animation before the emergence of celluloid film
Huygens, Christiaan. "Pour des representations par le moyen de verres convexes à la lampe" (in French). Rossell, Deac (2005). The Magic Lantern and Moving
Early_history_of_animation
Locally compact topological group with an invariant averaging operation
group by continuous affine transformations on a compact convex subset of a (separable) locally convex topological vector space has a fixed point. For locally
Amenable_group
and Q are probability distributions on the real line, such that P is absolutely continuous with respect to Q, i.e. P << Q, and whose first moments exist
Kullback's_inequality
Non-Japanese animation inspired by Japanese animation
com. May 11, 2025. Retrieved May 16, 2025. Moegirlpedia (May 6, 2025). "Convex Hero X". Moegirlpedia. Retrieved May 6, 2025. Pineda, Rafael Antonio (September
Anime-influenced_animation
Order of reptiles (fossil)
hyperphalangy. The flippers were not perfectly flat, but had a lightly convexly curved top profile, like an airfoil, to be able to "fly" through the water
Plesiosaur
Numerical analysis of electric power flow
flows and neglects reactive power flows. This method is non-iterative and absolutely convergent but less accurate than AC Load Flow solutions. DC power flow
Power-flow_study
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Boy/Male
Indian
Absolute.
Surname or Lastname
Italian
Italian : from the title of rank conte ‘count’ (from Latin comes, genitive comitis ‘companion’). Probably in this sense (and the Late Latin sense of ‘traveling companion’), it was a medieval personal name; as a title it was no doubt applied ironically as a nickname for someone with airs and graces or simply for someone who worked in the service of a count.English : variant of Count, cognate with 1.French : nickname for someone in the service of a count or for someone who behaved pretentiously, from Old French conte, cunte ‘count’ (of the same derivation as 1).French (Conté) : variant of Comté (see Comte).
Male
English
Anglicized form of Irish Gaelic Conláed, CONLEY means "purifying fire."
Surname or Lastname
Irish
Irish : variant spelling of Connor, now common in Scotland.English : occupational name for an inspector of weights and measures, Middle English connere, cunnere ‘inspector’, an agent derivative of cun(nen) ‘to examine’.
Boy/Male
British, Christian, English
Wagoner; To Convey
Boy/Male
Hindu
Absolute
Surname or Lastname
Spanish and Portuguese
Spanish and Portuguese : nickname from the title of rank conde ‘count’, a derivative of Latin comes, comitis ‘companion’.English : unexplained.
Boy/Male
Irish American
Strong willed or wise. Also a : Hero.
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Absolute
Male
English
Variant spelling of English Connor, CONNER means "hound-lover."
Boy/Male
Irish
Hero.
Surname or Lastname
English (Leicestershire)
English (Leicestershire) : variant of Culver.
Boy/Male
Irish American
Hound lover. Full of desire; much desire.
Surname or Lastname
English
English : habitational name from a place named Cove, examples of which are found in Devon, Hampshire, and Suffolk, from Old English cofa ‘cove’, ‘bay’, ‘inlet’, also ‘shelter’, ‘hut’, or a topographic name with the same meaning.
Surname or Lastname
English
English : metathesized form of the occupational name Coyner.English : possibly an occupational name for a dealer in rabbits or rabbit skins, from an agent derivative of Middle English cony ‘rabbit’ (see Coney).
Surname or Lastname
English
English : from Old French covine ‘fraud’, ‘deceit’, hence a derogatory nickname for a trickster.English : habitational name from a place in Staffordshire named Coven ‘(place) at the huts or shelters (Old English cofa, dative plural cofum)’.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Absolute
Boy/Male
Tamil
Keval Kumar | கேவலகà¯à®®à®¾à®°
Absolute
Keval Kumar | கேவலகà¯à®®à®¾à®°
Girl/Female
Australian, British, English, Indonesian
Absolutely and Ridiculously Perfect
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
Girl/Female
English American French
meaning favor; grace.
Boy/Male
Hindu
A name of a bird
Surname or Lastname
English
English : unexplained.Swedish : unexplained.
Boy/Male
Tamil
Daitya Sai | தைதà¯à®¯ ஸாஈ
Non Aryan
Girl/Female
Indian
Boy/Male
Hindu
Governor, Protector
Boy/Male
Hindu, Indian
Shiv
Boy/Male
Hindu, Indian, Marathi
Good Excellent Pious
Boy/Male
Gujarati, Hindu, Indian, Kannada
Life of the World; Worldly Life
Boy/Male
Tamil
Water like
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
ABSOLUTELY CONVEX-SET
dv.
In a convex form; convexly.
n. & v.
See Conge, Conge.
v. t.
To context.
adv.
In a convex form; as, a body convexly shaped.
a.
Made convex; protuberant in a spherical form.
v. t.
To accompany; to convoy.
a.
Loosed from any limitation or condition; uncontrolled; unrestricted; unconditional; as, absolute authority, monarchy, sovereignty, an absolute promise or command; absolute power; an absolute monarch.
a.
Pure; unmixed; as, absolute alcohol.
v. t.
To cause to pass from one place or person to another; to serve as a medium in carrying (anything) from one place or person to another; to transmit; as, air conveys sound; words convey ideas.
adv.
In an absolute, independent, or unconditional manner; wholly; positively.
a.
Convex on both sides; as, a biconvex lens.
n.
A convex body or surface.
a.
Complete in itself; perfect; consummate; faultless; as, absolute perfection; absolute beauty.
a.
Not immediately dependent on the other parts of the sentence in government; as, the case absolute. See Ablative absolute, under Ablative.
a.
Plane or flat on one side, and convex on the other; as, a plano-convex lens. See Convex, and Lens.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
v. t.
To impart or communicate; as, to convey an impression; to convey information.
a.
Convex on both sides; double convex. See under Convex, a.
a.
Convex on one side, and flat on the other; plano-convex.
a.
Viewed apart from modifying influences or without comparison with other objects; actual; real; -- opposed to relative and comparative; as, absolute motion; absolute time or space.