Monotonicity of Non-Pluripolar Monge-Ampere Masses

Abstract

We prove that on a compact Kahler manifold, the non-pluripolar Monge-Ampere mass of a theta-psh function decreases as the singularities increase. This was conjectured by Boucksom-Eyssidieux-Guedj-Zeriahi, who proved it under the additional assumption of the functions having small unbounded locus. As a corollary, we get a comparison principle for theta-psh functions, analogous to the comparison principle for psh functions due to Bedford-Taylor.