On the Convergence of Optimal Measures

TL;DR

This paper demonstrates that sequences of optimal measures for a weighted pluripotential problem on a compact set in complex space converge weak-* to the equilibrium measure, using recent theoretical results.

Contribution

It establishes the convergence of optimal measures to the equilibrium measure in weighted pluripotential theory, extending previous understanding with new theoretical insights.

Findings

Optimal measures converge weak-* to the equilibrium measure

The result applies to non-pluripolar compact sets in C^d

Uses recent advances by Berman and Boucksom

Abstract

Using recent results of Berman and Boucksom we show that for a non-pluripolar compact set K in C^d and an admissible weight function w=e^{-\phi} any sequence of so-called optimal measures converges weak-* to the equilibrium measure \mu_{K,\phi} of (weighted) Pluripotential Theory for K,\phi.