Talk:Amenable group

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You have new messages (last change).

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)


____

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; L^\infty 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 L^\infty 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)
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