On Beurling measure algebras

Abstract

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.

13 pages