Characterization, structure and analysis on Abelian \({\mathcal L}_{\infty}\) groups
An abelian topological group is an \({\mathcal L}_{\infty}\) group if and only if it is a locally \(\sigma\)-compact k-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian \({\mathcal L}_{\infty}\) group G is topologically isomorphic to \({\mathbb{R}}^{\alpha}\oplus G_ 0\) where \(\alpha \leq \aleph_ 0\) and \(G_ 0\) is an abelian \({\mathcal L}_{\infty}\) 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 \({\mathcal L}_{\infty}\) groups are given and their properties are studied.
scientific article; zbMATH DE number 3897561