|
|
|
|
|
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.
|
"filtration" is owned by CWoo. [ full author list (2) | owner history (1) ]
|
|
(view preamble | get metadata)
Cross-references: infinite chain, partial ordering, finite chain, inclusion, elements, sequence
There are 31 references to this entry.
This is version 5 of filtration, born on 2002-01-05, modified 2009-01-28.
Object id is 1331, canonical name is Filtration.
Accessed 8412 times total.
Classification:
| AMS MSC: | 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory ) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
