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I have been reading on Haar measure and we know that every locally compact Hausdorff group admits a Haar measure, is the same true for semigroups with identity $e$(monoid)? If not, is there a class of semigroups that admits a Haar measure?

Any help will be appreciated.

David Chan
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  • There are certainly classes of monoids where there is a Haar measure, those which incidentally happen to be groups for instance. If you want to try and work out what's going on to try and determine if there are other large classes where there are interesting things going on, I would recommend looking at a proof of the existence of Haar, this one http://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Gleason.pdf seems okay, and pick through the details to find out where specifically the inverse is being used. – user24142 May 20 '15 at 02:13

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