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...
30 KB (5,354 words) - 21:17, 4 October 2024
Borel set (redirect from Borel sigma algebra)
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...
13 KB (1,795 words) - 04:13, 6 October 2024
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...
18 KB (1,853 words) - 19:07, 30 August 2024
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
77 KB (12,096 words) - 17:40, 3 October 2024
Kolmogorov's zero–one law (redirect from Tail sigma algebra)
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...
6 KB (896 words) - 17:24, 27 April 2024
Pauli matrices (redirect from Sigma matrices)
sigma _{j},\sigma _{k}\right]+\{\sigma _{j},\sigma _{k}\}&=(\sigma _{j}\sigma _{k}-\sigma _{k}\sigma _{j})+(\sigma _{j}\sigma _{k}+\sigma _{k}\sigma...
45 KB (7,437 words) - 00:34, 24 September 2024
In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics...
51 KB (6,284 words) - 06:52, 22 September 2024
Measure (mathematics) (section Sigma-finite measures)
{\displaystyle \Sigma } a σ {\displaystyle \sigma } -algebra over X . {\displaystyle X.} A set function μ {\displaystyle \mu } from Σ {\displaystyle \Sigma } to...
35 KB (5,554 words) - 13:16, 1 September 2024
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...
5 KB (694 words) - 05:54, 3 October 2024
Filtration (mathematics) (redirect from Filtered sigma algebra)
\left\{{\mathcal {F}}_{t}\right\}_{t\geq 0}} of its σ {\displaystyle \sigma } -algebra F {\displaystyle {\mathcal {F}}} . A filtered probability space is...
13 KB (2,193 words) - 02:41, 4 May 2024
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...
10 KB (1,461 words) - 11:53, 27 July 2024
Y} are sets equipped with respective σ {\displaystyle \sigma } -algebras Σ {\displaystyle \Sigma } and T . {\displaystyle \mathrm {T} .} A function f :...
9 KB (1,329 words) - 00:07, 7 December 2023
3 } . {\displaystyle X=\{1,2,3\}.} One possible σ {\displaystyle \sigma } -algebra would be: F 1 = { X , ∅ } . {\displaystyle {\mathcal {F}}_{1}=\{X,\varnothing...
4 KB (531 words) - 14:27, 4 July 2024
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...
30 KB (4,256 words) - 14:00, 30 September 2024
\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...
15 KB (2,612 words) - 08:16, 12 September 2024
{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...
2 KB (333 words) - 16:10, 7 September 2024
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...
23 KB (4,160 words) - 15:09, 12 January 2024
mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex...
17 KB (2,618 words) - 03:51, 7 September 2024
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...
5 KB (566 words) - 15:23, 5 December 2023
overview, see Algebra. The bare word "algebra" may refer to: Elementary algebra Abstract algebra Algebra over a field In universal algebra, algebra has an axiomatic...
3 KB (415 words) - 17:08, 30 November 2021
Neumann algebras A: The set of all projectors is a σ {\displaystyle \sigma } -complete Boolean algebra, that is a pointfree σ {\displaystyle \sigma } -algebra...
10 KB (1,547 words) - 15:36, 16 February 2024
algebra Schur algebra Semisimple algebra Separable algebra Shuffle algebra Sigma-algebra Simple algebra Structurable algebra Supercommutative algebra...
2 KB (226 words) - 16:33, 17 January 2024
Field of sets (redirect from Set algebra)
complements Set function – Function from sets to numbers σ-algebra – Algebraic structure of set algebra Sigma-ideal – Family closed under subsets and countable...
23 KB (3,675 words) - 13:27, 30 October 2023
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...
6 KB (876 words) - 18:38, 18 August 2024
operation combining two topological spaces Join (sigma algebra), a refinement of sigma algebras Join (algebraic geometry), a union of lines between two varieties...
1 KB (208 words) - 01:30, 3 October 2024
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...
4 KB (764 words) - 23:27, 24 July 2024
Spinor (section Exterior algebra construction)
{\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...
72 KB (9,924 words) - 00:31, 24 September 2024
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...
10 KB (1,621 words) - 13:22, 4 October 2024
Non-associative algebra Outline of algebra Quaternion Rational function Relational algebra Representation theory Root of unity Scheme theory Sigma-algebra Singular...
134 KB (13,332 words) - 10:48, 6 October 2024
Predictable process (redirect from Predictable sigma-algebra)
respect to the σ-algebra generated by all left-continuous adapted processes. This σ-algebra is also called the predictable σ-algebra. Every deterministic...
3 KB (272 words) - 20:02, 23 September 2024