Category:Definitions/Sigma-Algebras

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This category contains definitions related to Sigma-Algebras.
Related results can be found in Category:Sigma-Algebras.


Let $X$ be a set.

A $\sigma$-algebra $\Sigma$ over $X$ is a system of subsets of $X$ with the following properties:

\((\text {SA} 1)\)   $:$   Unit:    \(\ds X \in \Sigma \)             
\((\text {SA} 2)\)   $:$   Closure under Complement:      \(\ds \forall A \in \Sigma:\) \(\ds \relcomp X A \in \Sigma \)             
\((\text {SA} 3)\)   $:$   Closure under Countable Unions:      \(\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:\) \(\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma \)             

Subcategories

This category has the following 3 subcategories, out of 3 total.

Pages in category "Definitions/Sigma-Algebras"

The following 36 pages are in this category, out of 36 total.