filtration

A filtration is a sequence of sets $A_1,A_2,\mathrm{\dots },A_n$ with

$$A_1\subset A_2\subset \mathrm{\cdots }\subset A_n.$$

If one considers the sets $A_1,\mathrm{\dots },A_n$ 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
Canonical name	Filtration
Date of creation	2013-03-22 12:08:38
Last modified on	2013-03-22 12:08:38
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	9
Author	CWoo (3771)
Entry type	Definition
Classification	msc 03E20
Related topic	FiltrationOfSigmaAlgebras