Harmonic measures for a point may form a square

Abstract

The paper deals with the compact convex set M of all representing measures with respect to the cone of potentials. The authors have recently proved (Adv.Math.218(4)(2008) 1181-1223) that the set of extreme points of M is a dense subset of M.

It was widely believed that M is a simplex, and hence a Poulsen simplex. This belief was disproved in the paper.

Keywords

• Harmonic measure
• Representing measure
• Simplex
• Square