Energy measure closability for Dirichlet forms

TL;DR

This paper proves the closability of symmetric Dirichlet forms with respect to energy dominant measures on various spaces, offering both elementary and potential theoretic proofs.

Contribution

It provides a new elementary proof for the closability of Dirichlet forms and discusses alternative potential theoretic methods.

Findings

Elementary proof of Dirichlet form closability

Use of potential theoretic results for alternative proof

Applicable to both locally compact and non-locally compact spaces

Abstract

We consider symmetric Dirichlet forms on locally compact and non-locally compact spaces and provide an elementary proof for their closability with respect to energy dominant measures. We also discuss how to use known potential theoretic results to furnish an alternative proof of this theorem.