Math Forum Discussions

David C. Ullrich

Posts: 21,553
Registered: 12/6/04

Re: Haar measure on locally compact group
Posted: Feb 6, 2013 2:32 PM

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On Wed, 6 Feb 2013 11:21:06 -0800 (PST), johnartin@gmail.com wrote:

>On Tuesday, February 5, 2013 4:17:15 PM UTC-6, john...@gmail.com wrote:
>> Hi,
>>
>>
>>
>> Can somebody help me by showing the outline or key steps to prove that if G is a locally compact group with the Haar measure (just assume G is Abelian), then if the Haar measure of G is finite, then G must be compact. I tried many times, got some progress but did not get to the final solution yet. Thanks
>
>I understand your proof, except that the notation near the end, I think we have to exchange the roles of x and y,

... yes, I got them switched, sorry.

>but the key is I understand the idea.
>All the standard book I read, this problem is an exercise...
>Thank you very much, I appreciate that.