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In mathematics, a superadditive set function is a set function whose value when applied to the union of two disjoint sets is greater than or equal to
Superadditive_set_function
Function from sets to numbers
mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values
Set_function
Property of a function
In mathematics, a function f {\displaystyle f} is superadditive if f ( x + y ) ≥ f ( x ) + f ( y ) {\displaystyle f(x+y)\geq f(x)+f(y)} for all x {\displaystyle
Superadditivity
subadditive. The maximum of additive set functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each i ∈ { 1 ,
Subadditive_set_function
Real function with secant line between points above the graph itself
f} is a convex function of one real variable, and f ( 0 ) ≤ 0 {\displaystyle f(0)\leq 0} , then f {\displaystyle f} is superadditive on the positive
Convex_function
Class of mathematical functions
Pseudo-Boolean function Topkis's theorem Submodular set function Superadditive Utility functions on indivisible goods Topkis, Donald M., ed. (1998). Supermodularity
Supermodular_function
Concept in game theory
_{i}(v)\leq v(\{i\})} . Similarly, if v {\displaystyle v} is a superadditive set function, i.e., if v ( S ∪ T ) ≥ v ( S ) + v ( T ) {\displaystyle v(S\cup
Shapley_value
an order: Subadditive function: for which the value of f (x + y) is less than or equal to f (x) + f (y). Superadditive function: for which the value of
List_of_types_of_functions
u} is a superadditive set function. Assuming u ( ∅ ) {\displaystyle u(\emptyset )} is non-positive, every supermodular function is superadditive. However
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
fractionally-subadditive valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log m ) 1 + ϵ m {\displaystyle
Welfare_maximization
the coalition size. An anonymous veto function is required to be a superadditive set function. Given a veto function v, an outcome x is blocked by a coalition
Veto_voting
Game where groups of players may enforce cooperative behaviour
grand coalition on smaller coalitions. Characteristic functions are often assumed to be superadditive (Owen 1995, p. 213). This means that the value of a
Cooperative_game_theory
Lemma concerning the limit of subadditive sequences
{ a n } n = 1 ∞ {\displaystyle \{a_{n}\}_{n=1}^{\infty }} is called superadditive if and only if for all m , n ∈ N {\displaystyle m,n\in \mathbb {N} }
Fekete's_lemma
Property of some mathematical functions
solution Choquet integral – Subadditive or superadditive integral Superadditivity – Property of a function Triangle inequality – Property of geometry
Subadditivity
Bounds of a sequence
in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively.
Limit inferior and limit superior
Limit_inferior_and_limit_superior
Product of numbers from 1 to n
Recherche Scientifiques. Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der
Factorial
is, φ ( ∅ ) = 0 {\displaystyle \varphi (\varnothing )=0} Superadditive: For any disjoint sets A {\displaystyle A} and B , {\displaystyle B,} φ ( A ∪ B
Inner_measure
Type of function in linear algebra
functional – Function made from a set Norm (mathematics) – Length in a vector space Seminorm – Mathematical function Superadditivity – Property of a function Proofs
Sublinear_function
Operation in calculus
subadditive or superadditive integral created by Gustave Choquet in 1953. The Bochner integral, a generalization of the Lebesgue integral to functions that take
Integral
Subadditive or superadditive integral
A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical
Choquet_integral
Group theory function
of finitely presented groups. In particular, if f(n) ≥ n4 is a superadditive function whose binary representation is computable in time O ( f ( n ) 4
Dehn_function
Generalization of a measure
_{i=1}^{n}A_{i}\right)\leq \sum _{i=1}^{n}\mu (A_{i}).} σ {\displaystyle \sigma } -Superadditivity: For any we A i ∈ A ( i = 1 , 2 , … ) {\displaystyle A_{i}\in {\mathcal
Content_(measure_theory)
share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR
Proportional_division
Theory of generalized measures in mathematics
E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that
Fuzzy_measure_theory
Physiological capacity
compared to the sum of each single modality together, an effect called the superadditive effect of multisensory integration. Neurons that respond to both visual
Sense
subadditivity condition above is instead replaced by the condition: Superadditivity: for X , Y ∈ H {\displaystyle X,Y\in {\mathcal {H}}} then E [ X ] +
Nonlinear_expectation
Criterion for fair division
share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR
Envy-freeness
Cognitive bias
Hu (2020) shows the endowment effect when the utility function is superadditive, i.e., the value of the whole is greater than the sum of its parts.
Endowment_effect
In mathematics, invariant of square matrices
Lin, Minghua; Sra, Suvrit (2014). "Completely strong superadditivity of generalized matrix functions". arXiv:1410.1958 [math.FA]. Paksoy; Turkmen; Zhang
Determinant
Concept in geometric group theory
a subgroup that is not locally finite has superadditive distortion; conversely every superadditive function (up to asymptotic equivalence) can be found
Subgroup_distortion
Probability theory for low quality data
expectations (previsions), aim to fill this gap. A lower probability function is superadditive but not necessarily additive, whereas an upper probability is
Imprecise_probability
Fair division problem for discrete items
Hence, every mFS-fair allocation is proportional. For every agent with superadditive utility, the MMSis worth at most 1 / n {\displaystyle 1/n} . Hence,
Fair_item_allocation
additive positive utilities, but also for any superadditive utilities, whether positive or negative: For superadditive utilities, there is a polynomial-time algorithm
Fair allocation of items and money
Fair_allocation_of_items_and_money
Ecological mechanism enabling species to coexist
competition on fitness does not change with the environment. If γ > 0 (superadditivity), it means that the adverse effects of competition during a bad year
Storage_effect
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SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
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SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
SUPERADDITIVE SET-FUNCTION
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