On Beurling measure algebras

TL;DR

This paper develops a measure-theoretic framework for Beurling measure algebras on weighted locally compact groups, filling a gap in the existing mathematical literature.

Contribution

It introduces a compatible measure theory for Beurling measure algebras on weighted locally compact groups, expanding the theoretical foundation.

Findings

Established a measure theory for regular compacted-Borel measures

Defined the Beurling measure algebra ${ m extbf{M}}(G, extbf{ extomega})$ within this framework

Filled a gap in the literature regarding measure algebras on weighted groups

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 ${\cal M}(G,\omega)$, thus filling a gap in the literature.