Approximations of convex bodies by measure-generated sets

Han Huang, Boaz A. Slomka

Given a Borel measure $\mu$ on ${\mathbb{R}}^n$, we define a convex set by \[ M(μ)=\bigcup_{\substack{0\le f\le1,\\ \int_{{\mathbb R}^{n}}f\,{\rm d}μ=1 } }\left\{ \int_{{\mathbb R}^…