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THEOREM A. Let A be a a-bounded subset and ,u a left-invariant Haar measure of a locally compact group G. Then there exists a sequence U. of bounded measurable neighborhoods of the unit e of G such that Ai*(AnUnx)/1i(Unx)->1, n-+oo for almost all x out of a measurable cover of A. The sequence Un may be chosen out of a given basis of bounded measurable neighborhoods and simultaneously for a countable family of sets A.

Three results for locally compact groups connected with Haar measure density theorem