Quantitative ergodic theorems for weakly integrable functions

TL;DR

This paper develops a quantitative pointwise ergodic theorem for weakly integrable functions, expanding the understanding of ergodic behavior in the context of trimmed Birkhoff sums.

Contribution

It introduces a new ergodic theorem applicable to weakly integrable functions with specific hypotheses, advancing ergodic theory.

Findings

Established a quantitative pointwise ergodic theorem for weakly integrable functions

Applied the theorem to trimmed Birkhoff sums

Extended ergodic results to broader classes of functions

Abstract

Under suitable hypotheses we establish a quantitative pointwise ergodic theorem which applies to trimmed Birkhoff sums of weakly integrable functions.