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Characterization, structure and analysis on Abelian groups. (English) Zbl 0563.43005
An abelian topological group is an group if and only if it is a locally σ-compact k-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian group G is topologically isomorphic to α G 0 where α 0 and G 0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra, L 1 -algebra, Fourier transforms of abelian groups are given and their properties are studied.

43A25Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A20L 1 -algebras on groups, semigroups, etc.
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