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Revision difference : filtration |
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| A {\em filtration} is a sequence of sets $A_1, A_2, \dots, A_n$ with |
A {\em filtration} is a sequence of sets $A_1, A_2, \dots, A_n$ with |
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| A_1 \subset A_2 \subset \cdots \subset A_n. |
A_1 \subset A_2 \subset \cdots \subset A_n. |
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$$ |
| 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. |
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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