# $\sigma$-algebra

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

• $X\in M$

• If $A\in M$ then $X-A\in M$.

• If $A_{1},A_{2},A_{3},\ldots$ is a countable subcollection of $M$, that is, $A_{j}\in M$ for $j=1,2,3,\ldots$ (the subcollection can be finite) then the union of all of them is also in $M$:

 $\bigcup_{j=1}^{\infty}A_{i}\in M.$
Title $\sigma$-algebra sigmaalgebra 2013-03-22 14:00:04 2013-03-22 14:00:04 drini (3) drini (3) 7 drini (3) Definition msc 28A60