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- W2068551869 abstract "The purpose of this note is to give a brief proof of the uniqueness (up to a positive multiple) of left Haar measure y (the existence of which we assume) on an arbitrary Hausdorff locally compact group G. The approach used here, employing the well-known device of an approximate identity, appears to be more transparent than any that we have found in the literature (e.g., [4, Theorem 29D, pp. 115-116] or [1, Theorem 1(B), pp. 15-16]). We remark that the elegant uniqueness proof for the Abelian case [5, 1.1.3, p. 2] cannot be improved upon; thus, our proof is of interest only for non-Abelian locally compact groups. We also observe that it is possible to give a combined existence and uniqueness proof (e.g., [2]). We begin with some notation. Let v denote a measure on G and let f, g be continuous functions on G with compact support. For such an f, let f'(y) = f(y-l); also, for x in G, let (Xf)(y) = f(x-ly). The convolution f * g is defined as usual (using the Haar measure 4):" @default.
- W2068551869 created "2016-06-24" @default.
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- W2068551869 date "1976-01-01" @default.
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- W2068551869 title "A short proof of the uniqueness of Haar measure" @default.
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- W2068551869 doi "https://doi.org/10.1090/s0002-9939-1976-0396914-8" @default.
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