Category:Sigma-Algebras

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This category contains results about Sigma-Algebras.
Definitions specific to this category can be found in Definitions/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:      \(\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:\) \(\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma \)             

Pages in category "Sigma-Algebras"

The following 35 pages are in this category, out of 35 total.