Spaces of quasi-invariant measures and convergence in them

TL;DR

This paper investigates the structure, topologies, and convergence properties of spaces of quasi-invariant measures, including their embeddings, metrizability, and associated uniform spaces, providing new theoretical insights.

Contribution

It introduces new results on the embeddings, metrizability, and convergence of quasi-invariant measure spaces, expanding understanding of their topological and uniform structures.

Findings

Conditions for metrizability of measure spaces

Theorems on convergence of nets of measures

Analysis of associated uniform spaces

Abstract

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant measures and their extensions are proved as well. Moreover, associated with them uniform spaces are studied.