filtration Filtration 2002-01-05 03:26:49 2009-01-28 00:21:11 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A {\em filtration} 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.