Talk:Filtration (mathematics)

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The concept is more general than the sigma-algebra case, though.

Charles Matthews 08:28, 15 Jun 2004 (UTC)

Not that I know of, so feel free to expand the article to the general case. Bryan Barnard 12:29, 3 Jul 2004 (UTC)

[edit] Need clarification

There appears to be an anomaly in the article. The definition mentions

"... subject only to the condition that if i ≤ j in I then Si is a subset of Sj"

whereas in the groups subsection of Examples in Algebra mentions

"A filtration of a group G, is then a sequence Gn of normal subgroups of G which is decreasing in the sense that for any n, we have Gn+1 ⊆ Gn."

According to the first statement, it should have been Gn ⊆ Gn+1.

Tsachin 13:16, 16 May 2007 (UTC)Tsachin

Let I be N with the reverse ordering. You get the same concept. Joeldl 13:47, 16 May 2007 (UTC)

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It would be nice to have some mention of I-stable module filtrations (for some ideal I), and how any two I-stable filtrations have bounded difference and hence induce the same topology (which is, of course, the I-topology). 128.148.41.116 (talk) 23:39, 5 May 2008 (UTC)

That is the Artin-Rees lemma. Joeldl (talk) 06:44, 6 May 2008 (UTC)