An inequality for the compositions of convex functions with convolutions and an alternative proof of the Brunn-Minkowski-Kemperman inequality

Takashi Satomi

Let $m(G)$ be the infimum of the volumes of all open subgroups of a unimodular locally compact group $G$. Suppose integrable functions ${\varphi }_1,{\varphi }_2:G\to [0,1]$ satisfy $\| ϕ_…