# On a Monge-Amp\`ere operator for plurisubharmonic functions with analytic singularities

## TL;DR

This paper investigates the continuity of generalized Monge-Ampère operators applied to plurisubharmonic functions with analytic singularities, providing new continuity results and a formula for total mass on compact Kähler manifolds.

## Contribution

It establishes continuity for decreasing sequences of such functions and derives a formula for their Monge-Ampère measure's total mass on compact Kähler manifolds.

## Key findings

- Proves continuity of Monge-Ampère operators for a natural class of functions.
- Derives a formula for the total mass of the Monge-Ampère measure.
- Provides insights into the behavior of plurisubharmonic functions with analytic singularities.

## Abstract

We study continuity properties of generalized Monge-Amp\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Amp\`ere measure of such a function on a compact K\"ahler manifold.