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'filtration'
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| Title of object: |
filtration |
| Canonical Name: |
Filtration |
| Type: |
Definition |
| Created on: |
2002-01-05 03:26:49 |
| Modified on: |
2005-04-03 23:10:45 |
| Classification: |
msc:03E20 |
Revision comment (for changes between this and next version):
| Changes for correction #14443 ('filtration of sigma algebras'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
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. |
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