Compact convex sets of the plane and probability theory

Jean-François Marckert, David Renault

The Gauss-Minkowski correspondence in ${\mathbb{R}}^2$ states the existence of a homeomorphism between the probability measures $\mu$ on $[0,2\pi ]$ such that ${\int }_0^{2\pi }{e}^{ix}d\mu (x)=0$…