$\sigma$-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 $A_1,A_2,A_3,\mathrm{\dots }$ 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	2013-03-22 14:00:04
Last modified on	2013-03-22 14:00:04
Owner	drini (3)
Last modified by	drini (3)
Numerical id	7
Author	drini (3)
Entry type	Definition
Classification	msc 28A60