ordered pair ( X , Σ ) {\displaystyle (X,\Sigma )} is called a measurable space. A σ-algebra of subsets is a set algebra of subsets; elements of the latter only...

type of algebra of sets known as σ-algebra (aka σ-field). Sigma algebra also includes terms such as: σ(A), denoting the generated sigma-algebra of a set...

G^{i}=[G^{i-1}]_{\delta \sigma }.} If i is a limit ordinal, set G i = ⋃ j < i G j . {\displaystyle G^{i}=\bigcup _{j<i}G^{j}.} The claim is that the Borel algebra is Gω1...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

countably infinite families of σ-algebras. For illustrative purposes, we present here the special case in which each sigma algebra is generated by a random variable...

number theory σ Sigma-algebra (σ-algebra, σ-field) in set theory A busy beaver function in computability theory Σ Σ n 0 {\displaystyle \Sigma _{n}^{0}} or...

especially in probability theory and ergodic theory, the invariant sigma-algebra is a sigma-algebra formed by sets which are invariant under a group action or...

{\displaystyle \Sigma } a σ {\displaystyle \sigma } -algebra over X . {\displaystyle X.} A set function μ {\displaystyle \mu } from Σ {\displaystyle \Sigma } to...

\left\{{\mathcal {F}}_{t}\right\}_{t\geq 0}} of its σ {\displaystyle \sigma } -algebra F {\displaystyle {\mathcal {F}}} . A filtered probability space is...

sigma _{j},\sigma _{k}\right]+\{\sigma _{j},\sigma _{k}\}&=(\sigma _{j}\sigma _{k}-\sigma _{k}\sigma _{j})+(\sigma _{j}\sigma _{k}+\sigma _{k}\sigma...