$\sigma $algebra
Let $X$ be a set. A $\sigma $algebra is a collection^{} $M$ of subsets of $X$ such that

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$X\in M$

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If $A\in M$ then $XA\in M$.

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If ${A}_{1},{A}_{2},{A}_{3},\mathrm{\dots}$ is a countable^{} subcollection of $M$, that is, ${A}_{j}\in M$ for $j=1,2,3,\mathrm{\dots}$ (the subcollection can be finite) then the union of all of them is also in $M$:
$$\bigcup _{j=1}^{\mathrm{\infty}}{A}_{i}\in M.$$
Title  $\sigma $algebra 

Canonical name  sigmaalgebra 
Date of creation  20130322 14:00:04 
Last modified on  20130322 14:00:04 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  7 
Author  drini (3) 
Entry type  Definition 
Classification  msc 28A60 