Bounded point evaluations for nonminimal measures (Q1110682)

A compactly supported positive measure \(\sigma\) in the complex plane \({\mathbb{C}}\) is said to be nonminimal if there is a compactly supported positive measure \(\mu\), not equal to \(\sigma\), with logarithmic potential equal to the logarithmic potential of \(\sigma\) outside some compact set and less than or equal to the logarithmic potential of \(\sigma\) on \({\mathbb{C}}\). If \(\sigma\) is a nonminimal measure then there is a nonempty open set, \(\Omega\), such that every sequence of polynomials converging in \(L^ 2(\sigma)\) converges normally on \(\Omega\).