Measure algebra M(G)

Summary

The measure algebra $M(G)$ of a locally compact group $G$ is the Banach space of finite complex Radon measures on $G$. Its product is the convolution of measures. It is a unital Banach $*$-algebra, whose unit is the point mass at the identity. It contains the group algebra $L^1(G)$ as a closed ideal and the point masses as a copy of $G$. It is the natural home of the Fourier–Stieltjes transform and of the multipliers of $L^1(G)$.