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...

or discrete spectrum Continuous spectrum Count data Discrete-time stochastic process Discrete geometry Discrete mathematics Discrete measure Discrete modelling...

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...

null. A σ {\displaystyle \sigma } -finite atomic measure μ {\displaystyle \mu } is called discrete if the intersection of the atoms of any atomic class...

probability theory treat discrete probability distributions and continuous probability distributions separately. The measure theory-based treatment of...

dimensions are used. Discrete time is often employed when empirical measurements are involved, because normally it is only possible to measure variables sequentially...

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...

sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure. Examples include...

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:...

{\displaystyle \delta _{\omega }} be the Dirac measure concentrated at ω {\displaystyle \omega } . Given a discrete probability distribution, there is a countable...

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one...

with discrete entropy. In terms of measure theory, the differential entropy of a probability measure is the negative relative entropy from that measure to...

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...

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric...

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies...

{\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...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

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...

be recovered from its discrete Fourier transform. The theory, introduced by Lev Pontryagin and combined with the Haar measure introduced by John von...

(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...

in the case of continuous random variables, or the counting measure in the case of discrete random variables). The underlying probability space Ω {\displaystyle...

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...

Descartes' theorem is Gauss–Bonnet where the curvature is a discrete measure, and Gauss–Bonnet for measures generalizes both Gauss–Bonnet for smooth manifolds...

Plancherel measure, such representations have positive measure. The name comes from the fact that they are exactly the representations that occur discretely in...

countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called...

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...

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...

λ < ∞ {\displaystyle -\infty <\lambda <\infty } . In the case of a discrete measure (in particular, when H is finite-dimensional), I = ∫ 1 d Ω T {\textstyle...

finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price...

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...