Uniform Continuity in Distribution for Borel Transformations of Random Fields

TL;DR

This paper provides simple sufficient conditions that guarantee the uniform continuity in distribution for Borel transformations of random fields, aiding in understanding their stability under transformations.

Contribution

It introduces new, straightforward criteria ensuring uniform continuity in distribution for Borel transformations of random fields.

Findings

Established sufficient conditions for uniform continuity in distribution.

Applied criteria to specific classes of random fields.

Enhanced understanding of stability properties under Borel transformations.

Abstract

Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.