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weighted locally compact group; group algebra; measure algebra; Beurling algebra
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.
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