# Monotonicity of non-pluripolar Monge-Amp\`ere masses

## TL;DR

This paper proves that on a compact Kähler manifold, the non-pluripolar Monge-Ampère mass decreases with increasing singularities of $ heta$-plurisubharmonic functions, extending previous results and establishing a comparison principle.

## Contribution

It establishes the monotonicity of non-pluripolar Monge-Ampère masses for $ heta$-psh functions without the small unbounded locus assumption, confirming a conjecture.

## Key findings

- Monge-Ampère mass decreases with increasing singularities.
- A comparison principle for $ heta$-psh functions is derived.
- Extension of Boucksom-Eyssidieux-Guedj-Zeriahi's conjecture.

## Abstract

We prove that on a compact K\"ahler manifold, the non-pluripolar Monge-Amp\`ere 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.