On Beurling measure algebras. (English) Zbl 07613029

Summary: We show how the measure theory of regular compacted-Borel measures defined on the \(\delta\)-ring of compacted-Borel subsets of a weighted locally compact group \((G,\omega)\) provides a compatible framework for defining the corresponding Beurling measure algebra \(\mathcal{M}(G,\omega)\), thus filling a gap in the literature.


43A10 Measure algebras on groups, semigroups, etc.
22D15 Group algebras of locally compact groups
43A05 Measures on groups and semigroups, etc.
43A20 \(L^1\)-algebras on groups, semigroups, etc.
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
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