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filtration (Definition)

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

$\displaystyle 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.



"filtration" is owned by djao.
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Cross-references: infinite chain, partial ordering, finite chain, inclusion, sequence
There are 28 references to this entry.

This is version 4 of filtration, born on 2002-01-05, modified 2005-04-03.
Object id is 1331, canonical name is Filtration.
Accessed 7273 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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