measurable space
91Schur test — In Mathematical Analysis,the Schur Test (named after German mathematician Issai Schur)is the name for the bound on the L^2 o L^2 operator normof an integral operator in terms of its Schwartz kernel(see Schwartz kernel theorem).The following… …
92Poisson random measure — Let (E, mathcal A, mu) be some measurable space with sigma finite measure mu. The Poisson random measure with intensity measure mu is a family of random variables {N A} {Ainmathcal{A defined on some probability space (Omega, mathcal F, mathrm{P}) …
93Stopped process — In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed (possibly random) time.DefinitionLet * (Omega, mathcal{F}, mathbb{P}) be a probability space; * (mathbb{X}, mathcal{A}) be a… …
94Killed process — In probability theory specifically, in stochastic analysis a killed process is a stochastic process that is forced to assume an undefined or killed state at some (possibly random) time. Definition Let X : T × Ω → S… …
95Inequalities in information theory — Inequalities are very important in the study of information theory. There are a number of different contexts in which these inequalities appear.hannon type inequalitiesConsider a finite collection of finitely (or at most countably) supported… …
96Khinchin's constant — In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x , the infinitely many denominators a i of the continued fraction expansion of x have an astonishing property: their geometric mean is a constant, known as… …
97Support — may refer to the following:* Sympathy, emotional support; * Technical support (a.k.a tech support) in computer hardware, software or electronic goods; * Support (mathematics), a kind of subset of the domain of a function; * Support (measure… …
98Algebra of random variables — In the algebraic axiomatization of probability theory, the primary concept is not that of probability of an event, but rather that of a random variable. Probability distributions are determined by assigning an expectation to each random variable …
99Sigma-ideal — In mathematics, particularly measure theory, a σ ideal of a sigma algebra ( σ , read sigma, means countable in this context) is a subset with certain desirable closure properties. It is a special type of ideal. Its most frequent application is… …
100Lebesgue's decomposition theorem — In mathematics, more precisely in measure theory, Lebesgue s decomposition theorem is a theorem which states that given mu and u two sigma; finite signed measures on a measurable space (Omega,Sigma), there exist two sigma; finite signed measures… …
