In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe") on a set X...

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...

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...

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

{\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...

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...

3 } . {\displaystyle X=\{1,2,3\}.} One possible σ {\displaystyle \sigma } -algebra would be: F 1 = { X , ∅ } . {\displaystyle {\mathcal {F}}_{1}=\{X,\varnothing...

Y} are sets equipped with respective σ {\displaystyle \sigma } -algebras Σ {\displaystyle \Sigma } and T . {\displaystyle \mathrm {T} .} A function f :...

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...

\Sigma _{0}} be an algebra of subsets of a set X . {\displaystyle X.} Consider a set function μ 0 : Σ 0 → [ 0 , ∞ ] {\displaystyle \mu _{0}:\Sigma _{0}\to...

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...

mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex...

{F}}_{t}\}} is called the σ-algebra of τ-past. If σ , τ {\displaystyle \sigma ,\tau } are two stopping times and σ ≤ τ {\displaystyle \sigma \leq \tau } almost...

Neumann algebras A: The set of all projectors is a σ {\displaystyle \sigma } -complete Boolean algebra, that is a pointfree σ {\displaystyle \sigma } -algebra...

by taking the power set of X {\displaystyle X} as the sigma-algebra Σ ; {\displaystyle \Sigma ;} that is, all subsets of X {\displaystyle X} are measurable...

complements Set function – Function from sets to numbers σ-algebra – Algebraic structure of set algebra Sigma-ideal – Family closed under subsets and countable...

these spaces. Denote by Σ 1 ⊗ Σ 2 {\displaystyle \Sigma _{1}\otimes \Sigma _{2}} the sigma algebra on the Cartesian product X 1 × X 2 {\displaystyle X_{1}\times...

is a function of another by the inclusion of the σ {\displaystyle \sigma } -algebras generated by the random variables. The usual statement of the lemma...

algebra Schur algebra Semisimple algebra Separable algebra Shuffle algebra Sigma-algebra Simple algebra Structurable algebra Supercommutative algebra...

additive but not vice versa, as shown below. Suppose that in addition to a sigma algebra A , {\textstyle {\mathcal {A}},} we have a topology τ . {\displaystyle...

operation combining two topological spaces Join (sigma algebra), a refinement of sigma algebras Join (algebraic geometry), a union of lines between two varieties...

{\displaystyle (-1)\{a_{1}\sigma _{1}+a_{2}\sigma _{2}\}\,(-1)=a_{1}\sigma _{1}+a_{2}\sigma _{2}} but a spinor rotation of 180°. The Clifford algebra Cℓ3,0( R {\displaystyle...

mathematics, the ba space b a ( Σ ) {\displaystyle ba(\Sigma )} of an algebra of sets Σ {\displaystyle \Sigma } is the Banach space consisting of all bounded...

mathematics, particularly measure theory, a 𝜎-ideal, or sigma ideal, of a σ-algebra (𝜎, read "sigma") is a subset with certain desirable closure properties...

Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those...

{F}}_{i}\right)_{i\in I}} be a filtration of the sigma algebra F {\displaystyle {\mathcal {F}}} ; ( S , Σ ) {\displaystyle (S,\Sigma )} be a measurable space, the state...