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...

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...

Sigma (/ˈsɪɡmə/ SIG-mə; uppercase Σ, lowercase σ, lowercase in word-final position ς; ‹See Tfd›Greek: σίγμα) is the eighteenth letter of the Greek alphabet...

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...

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

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, Sigma, Σ, σ, or ς in Wiktionary, the free dictionary. Sigma (Σ or σ, word-final lowercase ς) is the 18th letter of the Greek alphabet. Sigma may...

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

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

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

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...

theory and functional analysis — the cylindrical σ-algebra or product σ-algebra is a type of σ-algebra which is often used when studying product measures...

respect to the σ-algebra generated by all left-continuous adapted processes. This σ-algebra is also called the predictable σ-algebra. Every deterministic...

{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...

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

the sense of a locally finite measure on the Borel σ {\displaystyle \sigma } -algebra) μ {\displaystyle \mu } is called a moderate measure iff there are...

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

}}\sum _{\sigma \in {\mathfrak {S}}_{r+p}}\operatorname {sgn} (\sigma )t^{i_{\sigma (1)}\cdots i_{\sigma (r)}}s^{i_{\sigma (r+1)}\cdots i_{\sigma (r+p)}}{\mathbf...

displaying short descriptions of redirect targets Sigma-algebra – Algebraic structure of set algebraPages displaying short descriptions of redirect targets...

\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...

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

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

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...

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...

\Sigma } algebras, the direct product A = ∏ i ∈ I A i {\textstyle \mathbf {A} =\prod _{i\in I}\mathbf {A} _{i}} is a Σ {\displaystyle \Sigma } algebra...

algebra In measure theory: Algebra over a set, a collection of sets closed under finite unions and complementation Sigma algebra, a collection of sets closed...

{i} &=-\sigma _{2}\sigma _{3}=-i\sigma _{1}\\\mathbf {j} &=-\sigma _{3}\sigma _{1}=-i\sigma _{2}\\\mathbf {k} &=-\sigma _{1}\sigma _{2}=-i\sigma _{3}\end{aligned}}}...

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

S2CID 84897435 – via Cambridge University Press. Lowther, George (23 Nov 2009). "Sigma Algebras at a Stopping Time". Almost Sure at Wordpress. Archived from the original...

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...