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...

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; Ancient 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...

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...

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

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

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

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

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

{\displaystyle {\mathfrak {A}}(N,M)=\sigma (\operatorname {Cyl} (N,M))} is the σ-algebra generated by the cylinderical algebra. Let X {\displaystyle X} a Hausdorff...

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...

\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...

defining an algebra homomorphism Δ : A → A ⊗ A, and defining the tensor product representation as ρ = ( σ ⊗ τ ) ∘ Δ . {\displaystyle \rho =(\sigma \otimes...

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...

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

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...

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

{F}}_{i}=\sigma \left\{X_{j}^{-1}(B):j\leq i,B\in \Sigma \right\},} The sub-sigma-algebra F i {\displaystyle {\mathcal {F}}_{i}} can be understood as the sigma...

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...

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

{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...

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...

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...

principal value Measure (mathematics) Sigma algebra Separable sigma algebra Filtration (abstract algebra) Borel algebra Borel measure Indicator function Lebesgue...

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...

space ( X , F ) {\displaystyle (X,{\mathcal {F}})} , a σ {\displaystyle \sigma } -finite subset is a measurable subset which is the union of a countable...

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...

must be measurable with respect to some σ {\displaystyle \sigma } -algebra Σ {\displaystyle \Sigma } . In other words, for a given probability space ( Ω ...