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Mathematical concept
In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to
Counting_measure
Generalization of mass, length, area and volume
{\displaystyle \mathbb {C} } ) its Haar measure is the angle measure. For a discrete group the counting measure is a Haar measure. Every (pseudo) Riemannian manifold
Measure_(mathematics)
Stochastic way of assigning quantities across a space
the Dirac measure and X n {\displaystyle X_{n}} are random variables, is called a point process or random counting measure. This random measure describes
Random_measure
Inequality between integrals in Lp spaces
{\displaystyle S} is { 1 , … , n } {\displaystyle \{1,\dots ,n\}} with the counting measure, we have ∑ k = 1 n | x k y k | ≤ ( ∑ k = 1 n | x k | p ) 1 p ( ∑ k
Hölder's_inequality
Discrete-variable probability distribution
the counting measure, if it exists, is the Radon–Nikodym derivative of the pushforward measure of X {\displaystyle X} (with respect to the counting measure)
Probability_mass_function
Probability measure on a complex plane
mathematics, the Brown measure, named after Lawrence G. Brown, is a probability measure generalizing the normalized eigenvalue-counting measure (also called normalized
Brown_measure
Concept in measure theory
counting measure; the measure of any finite set is the number of elements in the set, and the measure of any infinite set is infinity. This measure is
Σ-finite_measure
Easily countable items
players. Counting measure – Mathematical concept Approximate number system – Innate ability to detect differences in magnitude without counting "Definition
Pip_(counting)
Japanese measure words used with numbers to count things, actions, and events
In Japanese, counter words or counters are measure words used with numbers to count things, actions, and events. Counters are added directly after numbers
Japanese_counter_word
Property of measure-preserving dynamical systems
{\displaystyle \mu } the product measure (each factor S {\displaystyle S} being endowed with its normalized counting measure). Then the shift operator T {\displaystyle
Ergodicity
Radon measure is locally finite. The counting measure is sometimes locally finite and sometimes not: the counting measure on the integers with their usual
Locally_finite_measure
Musical system of regularly occurring sounds
numbers may be termed count chant, "to identify it as a unique instructional process." In lieu of simply counting the beats of a measure, other systems can
Counting_(music)
Family of three random counting measures
Poisson-type random measures are a family of three random counting measures which are closed under restriction to a subspace, i.e. closed under thinning
Poisson-type_random_measure
Property of two measures in measure theory
Lebesgue measure. Look at some measurable space ( X , A ) {\displaystyle (X,{\mathcal {A}})} and let μ {\displaystyle \mu } be the counting measure, so μ
Equivalence_(measure_theory)
Finding the number of elements of a finite set
to each element. Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6
Counting
measures that occur in practice are σ-finite. Counting measure on an uncountable measure space with all subsets measurable is a decomposable measure that
Decomposable_measure
Theorem extending pre-measures to measures
the unit interval with Lebesgue measure and Y {\displaystyle Y} is the unit interval with the discrete counting measure. Let the ring R {\displaystyle
Carathéodory's extension theorem
Carathéodory's_extension_theorem
Software metric used to measure the size of a computer program
lines of code (LOC), is a software metric used to measure the size of a computer program by counting the number of lines in the text of the program's source
Source_lines_of_code
Duality for locally compact abelian groups
it carries an essentially unique natural measure, the Haar measure, which allows one to consistently measure the "size" of sufficiently regular subsets
Pontryagin_duality
Measure of total value one, generalizing probability distributions
Left-invariant (or right-invariant) measure on locally compact topological group Counting measure Lebesgue measure – Broadest definition of sizes in integer-dimensional
Probability_measure
Type of mathematical measure
are not examples of Radon measures: Counting measure on Euclidean space is an example of a measure that is not a Radon measure, since it is not locally
Radon_measure
Type of random mathematical object
process can be considered as a counting measure, so points processes are types of random measures known as random counting measures. In this context, the Poisson
Poisson_point_process
Number of words in a document or passage of text
wc, specifically for word counting. There are a wide variety of word counting tools available online. Different word counting programs may give varying
Word_count
Mathematical notation used in probability and statistics
interpreted as random sequences of points, random sets of points or random counting measures. In some mathematical frameworks, a given point process may be considered
Point_process_notation
Measurement of cell concentration
Cell counting is any of various methods for the counting or similar quantification of cells in the life sciences, including medical diagnosis and treatment
Cell_counting
Multi-cultural system of counting directly involving the digits
Finger-counting or dactylonomy is counting using the fingers. Various systems have existed over time and across cultures, although many have declined
Finger-counting
Generalization of volume to non-integer number of dimensions
set. Thus, the concept of the Hausdorff measure generalizes the Lebesgue measure and its notions of counting, length, and area. It also generalizes volume
Hausdorff_measure
Measure space in mathematics
decomposable into measures on continua, and a finite or countable counting measure. Inner measure Lebesgue measurable set – Broadest definition of sizes in integer-dimensional
Complete_measure
Branch of mathematics concerning probability
respect to this dominating measure. Discrete densities are usually defined as this derivative with respect to a counting measure over the set of all possible
Probability_theory
Left-invariant (or right-invariant) measure on locally compact topological group
and a (left and right invariant) Haar measure on G {\displaystyle G} is the counting measure. The Haar measure on the topological group ( R , + ) {\displaystyle
Haar_measure
motives (see below). If the ground field is finite, and one applies the counting measure to Z ( X , t ) {\displaystyle Z(X,t)} , one obtains the local zeta
Motivic_zeta_function
Mathematical theorem regarding decomposability of measure spaces
parts," using the counting measure on some discrete space. The theorem is due to Dorothy Maharam. It was extended to localizable measure spaces by Irving
Maharam's_theorem
Triangle inequality in Lp spaces
inequality can be specialized to sequences and vectors by using the counting measure: ( ∑ k = 1 n | x k + y k | p ) 1 / p ≤ ( ∑ k = 1 n | x k | p ) 1 /
Minkowski_inequality
Minimal measurable set with positive measure
{P}}(\mathbb {R} ),\nu )} where ν {\displaystyle \nu } denotes the counting measure. This space is atomic, with all atoms being the singletons, yet the
Atom_(measure_theory)
Mathematical function in measure theory
be the counting measure on this measurable space and define μ := ∑ n = 1 ∞ ν n . {\displaystyle \mu :=\sum _{n=1}^{\infty }\nu _{n}.} The measure μ {\displaystyle
S-finite_measure
Systems for measuring textiles
thread count (a measure of the coarseness or fineness of fabric), in ends per inch (e.p.i) and picks per inch (p.p.i). Micronaire is a measure of the
Units_of_textile_measurement
Principle in Bayesian statistics
defined relative to a specified measure or prior. In discrete cases, Shannon entropy is defined relative to the counting measure (or an explicitly specified
Principle_of_maximum_entropy
Measurement for ionizing radiation
for when relating cpm to dpm. This is known as the counting efficiency. The factors affecting counting efficiency are shown in the accompanying diagram
Counts_per_minute
Words that measure quantities
as measure words. One can also say "three pails of shells"; in this case the measure word pails accompanies a count noun (shells). The term measure word
Measure_word
Statistics concept
the coefficient of variation, is a measure of the dispersion of a counting process. It was originally used to measure the Fano noise in ion detectors. It
Fano_factor
Measurement of radioactivity within the body
where N is the number of counts of background in the region of interest; E is the counting efficiency; and T is the counting time. This quantity is approximately
Whole-body_counting
Measure for Baire sets in mathematics
measure. On compact (or σ-compact) metric spaces, Borel sets are the same as Baire sets and Borel measures are the same as Baire measures. Counting measure
Baire_measure
data warehouse, a measure is a property on which calculations (e.g., sum, count, average, minimum, maximum) can be made. A measure can either be categorical
Measure_(data_warehouse)
Instrument to measure light intensity
photodiode, or photomultiplier. Some models employ photon counting, measuring light by counting individual photons. They are especially useful in areas
Photometer
Unit of time equal to 60 minutes
the hour length and count using some of these older definitions and counting methods. In ancient and medieval cultures, the counting of hours generally
Hour
Used to count, measure, and label
A number is a mathematical object used to count, measure, order and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth
Number
Function spaces generalizing finite-dimensional p norm spaces
measure (e.g. the counting measure). Neither condition holds for the Lebesgue measure on the real line while both conditions holds for the counting measure
Lp_space
Construction in measure theory
product measure. Take the product X×Y, where X is the unit interval with Lebesgue measure, and Y is the unit interval with counting measure and all sets
Product_measure
Device that counts people as they pass
With video counting technology, the expected accuracy rate of the device is 80% to 95%. Crowd counting Human presence detection Traffic count "Metrics for
People_counter
Smallest value a measuring instrument can measure
least count of a measuring instrument is the smallest value in the measured quantity that can be resolved on the instrument's scale. The least count is related
Least_count
Type of measure in measure theory
\varnothing ,\mu (U)>0.} Counting measure on any set X {\displaystyle X} (with any topology) is strictly positive. Dirac measure is usually not strictly
Strictly_positive_measure
Proposition in statistics
{\displaystyle \,x~} . The density function may be a density with respect to counting measure, i.e. a probability mass function. Two likelihood functions are equivalent
Likelihood_principle
Random set of points on a space with random number and random position
mathematical interpretations of a point process, such as a random counting measure or a random set, and different notations. The notations are described
Point_process
Vector space of infinite sequences
are special cases of L p {\displaystyle L^{p}} spaces for the counting measure on the set of natural numbers. Other important classes of sequences
Sequence_space
Korean words for counting things
The Korean language uses special measure words or counting words for specific objects and events. These suffixes are called subullyusa (수분류사; 數分類詞) in
Korean_count_word
Description of continuous random distribution
reference measure is the Lebesgue measure. The probability mass function of a discrete random variable is the density with respect to the counting measure over
Probability_density_function
Space of bounded sequences
}=L^{\infty }(\mathbb {N} )} where the natural numbers are equipped with the counting measure. One application of ℓ ∞ {\displaystyle \ell ^{\infty }} and L ∞ {\displaystyle
L-infinity
measurement of ionising radiation the counting efficiency is the ratio between the number of particles or photons counted with a radiation counter and the
Counting_efficiency
Process of counting votes in an election
Vote counting is the process of counting votes in an election. It can be done manually or by machines. In the United States, the compilation of election
Vote_counting
Lebesgue measure Lebesgue integration Lebesgue's density theorem Counting measure Complete measure Haar measure Outer measure Borel regular measure Radon
List of integration and measure theory topics
List_of_integration_and_measure_theory_topics
in relation to a point process, which can be interpreted as random counting measures, and has applications in characterizing and deriving results on point
Laplace_functional
Inventory auditing procedure
operations to count all items simultaneously. By focusing on a subset of items, cycle counting is less disruptive to daily operations. Most cycle counting applications
Cycle_count
Computationally feasible measure in real-valued number of dimensions
not a measure. In particular, the m-dimensional Minkowski content in Rn is not a measure unless m = 0, in which case it is the counting measure. Indeed
Minkowski_content
Expressing a measure as an integral of another
fails to hold. Consider the Borel σ-algebra on the real line. Let the counting measure, μ, of a Borel set A be defined as the number of elements of A if A
Radon–Nikodym_theorem
Measurement of the human penis
Human penis size varies on a number of measures, including length and circumference when flaccid and erect. Besides the natural variability of human penises
Human_penis_size
Pandemic caused by SARS-CoV-2
Multiple measures are used to quantify mortality. Official death counts typically include people who died after testing positive. Such counts exclude deaths
COVID-19_pandemic
issue often called 'double counting', wherein the total value of a good is included several times in national output, by counting it repeatedly in several
Measures of national income and output
Measures_of_national_income_and_output
Term in geometry and fractal analysis
both types of box counting. The data gathered for each ε {\displaystyle \varepsilon } are manipulated to calculate lacunarity. One measure, denoted here as
Lacunarity
Average uncertainty in variable's states
entropy, where the measure m is the counting measure, and the differential entropy, where the measure m is the Lebesgue measure. If the measure m is itself a
Entropy_(information_theory)
Theory and paradigm of statistics
if π ≪ ν {\displaystyle \pi \ll \nu } (absolutely continuous w.r.t. counting measure), analogous we can write: Q ( x ) = ∫ Θ P θ ′ ( x ) ⋅ π ( θ ′ ) d ν
Bayesian_statistics
Average income of an economy
Besharov, Douglas J.; Couch, Kenneth A. (eds.). Counting the poor: new thinking about European poverty measures and lessons for the United States. International
Per_capita_income
Algorithm used by Google Search to rank web pages.
Larry Page. PageRank is a way of measuring the importance of website pages. According to Google: PageRank works by counting the number and quality of links
PageRank
Measure in functional analysis
space. The index set I {\displaystyle I} becomes a measure space when endowed with its counting measure (which we shall denote by μ {\displaystyle \mu }
Lp_sum
Axiom in set theory
{\displaystyle (\Omega ,2^{\Omega },\nu )} is a measure space where ν {\displaystyle \nu } is the counting measure and f : Ω → R {\displaystyle f:\Omega \to
Axiom_of_finite_choice
Calendar era based on the birth of Jesus
date by the Spanish Era (also called Era of the Caesars), which began counting from 38 BC, well into the Middle Ages. In 1422, Portugal became the last
Anno_Domini
Country in Western Europe
of the world; it is about 2,586 square kilometres (998 sq mi) in size, measuring 82 km (51 mi) long and 57 km (35 mi) wide. It lies between latitudes 49°
Luxembourg
Alaska Measure 2 was a ballot initiative narrowly approved by voters in Alaska as part of the 2020 United States elections. The proposal switched Alaska's
2020_Alaska_Measure_2
Method of determining fractal dimension
fractal lying on an evenly spaced grid and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this
Minkowski–Bouligand_dimension
2021 attack to stop election certification
sought to keep him in power by preventing a joint session of Congress from counting the Electoral College votes to formalize the victory of then president-elect
January 6 United States Capitol attack
January_6_United_States_Capitol_attack
Result in geometry
consider a finite subset of Euclidean space and replace Lebesgue measure by counting measure. The following proof is the original one Proof Overview: We prove
Loomis–Whitney_inequality
Number used for counting
"counting to 10"), or by applying the count to objects (as in "counting the students in the class"). When applied to a collection of objects, counting
Natural_number
West Germanic language
The English lexicon consists of around 170,000 words (or 220,000, if counting obsolete words), according to an estimate based on the 1989 edition of
English_language
Addition of several numbers or other values
a} to b {\displaystyle b} , and where μ {\displaystyle \mu } is the counting measure over the integers. Given a function f that is defined over the integers
Summation
Elements in exactly one of two sets
two sets can be considered a measure of how "far apart" they are. First consider a finite set S and the counting measure on subsets given by their size
Symmetric_difference
Mathematical statistics distance measure
as counting measure for discrete distributions, or Lebesgue measure or a convenient variant thereof such as Gaussian measure or the uniform measure on
Kullback–Leibler_divergence
Rate or speed at which a language is spoken
Speech tempo is a measure of the number of speech units of a given type produced within a given amount of time. Speech tempo is believed to vary within
Speech_tempo
Electronic measuring instrument
technique. Period measurement is done by measuring the time required for an integer number of cycles, rather than counting cycles for a constant gate time, and
Frequency_counter
Area that observes a uniform standard time
Egyptian sundial was used to measure laborers' work hours. In the 2nd century BC, Hipparchus developed a method to measure longitudinal distances by comparing
Time_zone
Topics referred to by the same term
mechanical components Tally counter, a mechanical counting device Web counter, a counter that counts the number of visits to a web page Project COUNTER
Counter
Concept in probability theory
countable Markov process example where ν {\displaystyle \nu } was the counting measure. Moreover it encompasses other important examples such as the convolution
Markov_kernel
1867–1918 dual monarchy in Central Europe
to prevent the Russians from expanding into nearby Serbia. In another measure to keep the Russians out of the Balkans, Austria–Hungary formed an alliance
Austria-Hungary
more stringent: for instance, the University of California, Berkeley, only counts current and retired faculty members, while the University of Chicago includes
List of Nobel laureates by university affiliation
List_of_Nobel_laureates_by_university_affiliation
number ones. If counting only entries after the creation of Billboard Hot 100, Presley has seven number-one singles on the chart. If counting Drake's uncredited
List of Billboard Hot 100 chart achievements and milestones
List_of_Billboard_Hot_100_chart_achievements_and_milestones
Decennial census mandated by the US Constitution
the "respective Numbers" of the "several States" will be determined by "counting the whole number of persons in each State, excluding Indians not taxed
United_States_census
Counting of the days from Passover to Shavuot
omer still has a purpose as a remembrance of the counting up to Sinai. One explanation for the Counting of the Omer is that it shows the connection between
Counting_of_the_Omer
Theorem of convex functions
\mathbb {N} } dividing n. Let Ω = {x1, ... xn}, and take μ to be the counting measure on Ω, then the general form reduces to a statement about sums: φ (
Jensen's_inequality
2018 familicide in Colorado
pushed through a hatch at the top of a different tank, with the opening measuring 8 inches (20 centimetres) in diameter. According to the medical examiner
Watts_family_murders
English actor (born 1978)
the Sun, all for the National Theatre. In 2010 he played Angelo in Measure for Measure at the Almeida Theatre. Later in 2010, he played the title role in
Rory_Kinnear
Measure of the structural complexity of a software program
metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent paths through a program's source
Cyclomatic_complexity
SI unit of temperature
with air thermometers for most purposes. Specifically, "the numerical measure of temperature shall be simply the mechanical equivalent of the thermal
Kelvin
travel, tourism, insurance
COUNTING MEASURE
COUNTING MEASURE
Surname or Lastname
English
English : occupational name from Old English hunting, a derivative of huntian ‘to hunt’.
Girl/Female
Indian
Chanting
Surname or Lastname
English (southern counties)
English (southern counties) : from a Middle English personal name, a pet form of Peter. Compare Parrott.
Surname or Lastname
English (eastern counties)
English (eastern counties) : apparently a variant of German.
Surname or Lastname
English
English : variant spelling of Countess.
Surname or Lastname
English
English : patronymic from a short form of the personal name Cudbert (see Cuthbert).Americanized spelling of German Kötting or the variant Kotting (see Koetting).
Boy/Male
Arabic, Muslim, Sindhi
Ascension; Rising; Mounting
Surname or Lastname
English (southern counties)
English (southern counties) : unexplained.German : patronymic form of Old 2.
Boy/Male
Hindu, Indian
Counting
Boy/Male
Muslim/Islamic
Ascension Mounting Rising
Girl/Female
Indian, Sanskrit
Chanting
Surname or Lastname
English (eastern counties)
English (eastern counties) : unexplained. Possibly a variant of Masset (see Massett).
Surname or Lastname
English (southern counties)
English (southern counties) : apparently a variant of Hapgood.
Surname or Lastname
English
English : nickname from some fancied resemblance to the songbird (Emberiza spp.).German : patronymic from an unexplained Frisian-Lower Saxon personal name, or a derivative of Bunt- (see Bunten).Sarah Bunting (1686–1762), born in Matlock, Derbyshire, became a noted Quaker minister in Cross Wicks, NJ. It is believed but not certain that other members of her family, including her father, John Bunting, came with her to NJ sometime before 1704, when her marriage to William Murfin is recorded.
Surname or Lastname
English (eastern counties)
English (eastern counties) : unexplained.
Surname or Lastname
English (mainly northeastern counties)
English (mainly northeastern counties) : variant of Latham.
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Telugu
Chanting
Surname or Lastname
English (southern counties)
English (southern counties) : from Middle English woderson ‘son of the woodman’.
Surname or Lastname
English (southern counties)
English (southern counties) : nickname from Middle English ferette, fyrette ‘ferret’, literally ‘little thief’ (Old French fuiret, furet).
Surname or Lastname
English (northeastern counties)
English (northeastern counties) : unexplained. Compare Hedgepeth.
COUNTING MEASURE
COUNTING MEASURE
COUNTING MEASURE
COUNTING MEASURE
COUNTING MEASURE
COUNTING MEASURE
COUNTING MEASURE
travel, tourism, insurance