A compactness result in approach theory with an application to the continuity approach structure

TL;DR

This paper proves a new compactness theorem within approach theory and applies it to extend Prokhorov's Theorem for the continuity approach structure, broadening the understanding of measure convergence.

Contribution

It introduces a novel compactness result in approach theory and generalizes Prokhorov's Theorem for the continuity approach structure.

Findings

Established a compactness result in approach theory.

Generalized Prokhorov's Theorem for the continuity approach structure.

Enhanced understanding of measure convergence in approach spaces.

Abstract

We establish a compactness result in approach theory which we apply to obtain a generalization of Prokhorov's Theorem for the continuity approach structure.