The Topology on the Space of δ-psh Functions in the Cegrell Classes

Abstract

The aim of the present paper is to introduce a metric locally convex topology on the space \({\delta \mathcal{E} = \mathcal{E}{\text{ - }}\mathcal{E}}\) of δ-psh functions in the Cegrell class \({\mathcal{E}}\). We prove that with this topology \(\delta \mathcal{E}\) is a non-separable and non-reflexive Frechet space. At the same time, we extend the Monge–Ampere operator from the class \(\mathcal{E}\) to \(\delta \mathcal{E}\).