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# filtration

A 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.

Related:

FiltrationOfSigmaAlgebras

Type of Math Object:

Definition

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Reference

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## Mathematics Subject Classification

03E20*no label found*

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