# filtration

A is a sequence of sets $A_{1},A_{2},\dots,A_{n}$ with

 $A_{1}\subset A_{2}\subset\cdots\subset A_{n}.$

If one considers the sets $A_{1},\dots,A_{n}$ as elements of a larger set which are partially ordered by inclusion, then a filtration is simply a finite chain with respect to this partial ordering. It should be noted that in some contexts the word “filtration” may also be employed to describe an infinite chain.

Title filtration Filtration 2013-03-22 12:08:38 2013-03-22 12:08:38 CWoo (3771) CWoo (3771) 9 CWoo (3771) Definition msc 03E20 FiltrationOfSigmaAlgebras