Classification and Metrization of Classes of Smooth measures

TL;DR

This paper classifies various classes of smooth measures based on properties like denseness and locality, explores their relationships, and introduces a new metric to analyze the Revuz correspondence's continuity.

Contribution

It provides a new classification framework for smooth measures and introduces the Miyadera metric to study their properties and relationships.

Findings

Classified smooth measures by denseness and locality.

Established relationships among Kato class and Radon measures.

Introduced Miyadera metric and proved Revuz correspondence continuity.

Abstract

We classify the several classes of the set of smooth measures from the perspective of the denseness and the locality, and consider their relationships, in particular, that of the Kato class and Radon measures of finite energy integrals. We also introduce the Miyadera metric on the Dynkin class, and obtain the continuity of the Revuz correspondence.