mathematics, more precisely in measure theory, a measure on the real line is called a discrete measure (in respect to the Lebesgue measure) if it is concentrated...
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or discrete spectrum Continuous spectrum Count data Discrete-time stochastic process Discrete geometry Discrete mathematics Discrete measure Discrete modelling...
11 KB (1,327 words) - 10:28, 22 May 2025
a measure on the real line is called a discrete measure (in respect to the Lebesgue measure) if its support is at most a countable set. Discrete measure...
6 KB (640 words) - 04:31, 19 December 2022
sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure. Examples include...
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Probability mass function (redirect from Discrete probability space)
probability mass function of a discrete random variable X {\displaystyle X} can be seen as a special case of two more general measure theoretic constructions:...
10 KB (1,539 words) - 19:51, 12 March 2025
Probability theory (redirect from Measure-theoretic probability theory)
probability theory treat discrete probability distributions and continuous probability distributions separately. The measure theory-based treatment of...
26 KB (3,591 words) - 11:44, 23 April 2025
null. A σ {\displaystyle \sigma } -finite atomic measure μ {\displaystyle \mu } is called discrete if the intersection of the atoms of any atomic class...
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Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection...
26 KB (2,771 words) - 14:34, 10 May 2025
decomposes a singular measure into a singular continuous measure and a discrete measure. See below for examples. As a particular case, a measure defined on the...
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Probability distribution (redirect from Discrete probability distribution)
{\displaystyle \delta _{\omega }} be the Dirac measure concentrated at ω {\displaystyle \omega } . Given a discrete probability distribution, there is a countable...
48 KB (6,688 words) - 17:43, 6 May 2025
dimensions are used. Discrete time is often employed when empirical measurements are involved, because normally it is only possible to measure variables sequentially...
10 KB (1,535 words) - 10:04, 10 January 2025
discrete group is discrete. every quotient of a discrete group is discrete. the product of a finite number of discrete groups is discrete. a discrete...
7 KB (899 words) - 11:34, 23 October 2024
Plancherel measure, such representations have positive measure. The name comes from the fact that they are exactly the representations that occur discretely in...
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Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric...
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with discrete entropy. In terms of measure theory, the differential entropy of a probability measure is the negative relative entropy from that measure to...
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number (cf. picture). It is the cumulative distribution function of the discrete measure on the rational numbers, where a i {\displaystyle a_{i}} is the weight...
19 KB (2,471 words) - 01:32, 25 January 2025
Spectrum (physical sciences) (redirect from Discrete spectrum)
spectrum domain (such as frequency or wavelength) or discrete if it attains non-zero values only in a discrete set over the independent variable, with band gaps...
22 KB (2,734 words) - 20:30, 23 May 2025
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...
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Pontryagin duality (section Haar measure)
be recovered from its discrete Fourier transform. The theory, introduced by Lev Pontryagin and combined with the Haar measure introduced by John von...
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with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted...
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Random variable (redirect from Discrete random variable)
in the case of continuous random variables, or the counting measure in the case of discrete random variables). The underlying probability space Ω {\displaystyle...
42 KB (6,634 words) - 15:00, 24 May 2025
finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price...
16 KB (2,684 words) - 04:31, 23 April 2025
Descartes' theorem is Gauss–Bonnet where the curvature is a discrete measure, and Gauss–Bonnet for measures generalizes both Gauss–Bonnet for smooth manifolds...
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topology) and the real line with the discrete topology is a locally compact group with the product topology and a Haar measure on this group is not inner regular...
32 KB (5,375 words) - 03:20, 9 June 2025
mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable...
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Geometry (redirect from Geometric measure)
(geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') is a branch of mathematics concerned with properties of space such as...
102 KB (10,101 words) - 17:40, 10 June 2025
A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant...
18 KB (2,282 words) - 02:30, 25 May 2025
Convolution (redirect from Discrete convolution)
similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f ∗ g {\displaystyle f*g} differs from cross-correlation...
67 KB (8,819 words) - 15:20, 10 May 2025
both the discrete entropy, where the measure m is the counting measure, and the differential entropy, where the measure m is the Lebesgue measure. If the...
72 KB (10,220 words) - 13:03, 6 June 2025
Wilson polynomials. Discrete orthogonal polynomials are orthogonal with respect to some discrete measure. Sometimes the measure has finite support, in...
15 KB (2,079 words) - 21:55, 22 May 2025