Abstract
It is shown that the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact. It turns out that these groups, in many respects, behave like locally compact groups. Suitably modified, many theorems from harmonic analysis carry over to this case. A few applications are given and some open problems are mentioned.
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Reference
J. P. R. Christensen,Borel structures in groups and semigroups, Math. Scand.28 (1971), 124–128.
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Christensen, J.P.R. On sets of Haar measure zero in abelian polish groups. Israel J. Math. 13, 255–260 (1972). https://doi.org/10.1007/BF02762799
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DOI: https://doi.org/10.1007/BF02762799