Talk:Amenable group
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I simply took it from PlanetMath, let me know if it is not ok by some reason, they seem to hve GLP as well, but maybe a bit different flavor...
Tosha 01:03, 16 May 2004 (UTC)
PlanetMath should be OK - as far as I know. Just add a link to the original article. Charles Matthews 08:34, 16 May 2004 (UTC)
It needs rewriting anyway..
- Amenability makes sense for any toplogical group, and the notion is used in that generality
- Missing is Folner's condition.
CSTAR 00:07, 17 May 2004 (UTC)
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I agree, but I think it is already something to start from.
Tosha 10:51, 19 May 2004 (UTC)
There are 12 or more conditions equivalent to amenability listed in an encyclopedia (the Soviet one) ... we should get writing ...
Charles Matthews 10:53, 19 May 2004 (UTC)
[edit] Simplified definition
I've added the simplified definition for discrete groups. There's a whole branch of math, geometric group theory, where groups are always discrete. We (geometric group theorists) totally ignore the possibility of topological groups; 
scares us.
I'd like to see the article reorganized to emphasize that both definitions are equally legitimate in different contexts. Right now, the organization makes it look like the definition is the main one. (Although I agree it is more general than the discrete version.) Done.
Finally, my apologies if there's a mistake in the definition I added. I'll check it against a reference soon.
Dbenbenn 15:22, 4 Nov 2004 (UTC)
- Apparently "soon" means "three months later". I found and corrected a small error. Unfortunately, my reference is not currently citable. I'll add the citation eventually. dbenbenn | talk 00:43, 13 Feb 2005 (UTC)
- It might be a good idea to refer to the "measure" in the second definition as a "finitely-additive measure" since most of the time, "measure" means countably-additive. It's confusing, since interesting amenable groups generally *do not* have countably-additive left-invariant probability measures.--Mattday 02:42, 26 September 2005 (UTC)
