A measure theoretic approach to Lipschitz regularity and its Haar type wavelet analysis

TL;DR

This paper extends the characterization of Lipschitz regularity to non-atomic probability spaces using measure theory and Haar wavelet analysis, broadening the understanding of function regularity in more general settings.

Contribution

It introduces a measure theoretic approach to Lipschitz regularity and applies Haar wavelet analysis to non-atomic probability spaces, advancing the theoretical framework.

Findings

Extended Lipschitz regularity characterization to non-atomic spaces

Utilized generalized Haar systems for analysis

Provided new insights into wavelet-based regularity measures

Abstract

In this note, we extend the characterization of dyadic Lipschitz regularity of functions to non-atomic probability spaces, using generalized Haar systems.