Explore: Sigma Algebra

a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used

the Borel algebra can be generated from the class of open sets by iterating the operation G ↦ G δ σ {\displaystyle G\mapsto G_{\delta \sigma }} to the

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

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

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

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

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

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center

recognized." Let X {\displaystyle X} be a set and Σ {\displaystyle \Sigma } a σ-algebra over X {\displaystyle X} , defining subsets of X {\displaystyle X}

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