# A detailed proof of Bourgain's Return Times Theorem

## TL;DR

This paper provides a comprehensive proof of Bourgain's Return Times Theorem and extends it to systems with purely atomic invariant sigma-algebras, enhancing understanding of recurrence in dynamical systems.

## Contribution

It offers a detailed proof of Bourgain's theorem and generalizes the result to a broader class of systems with atomic invariant sigma-algebras.

## Key findings

- Detailed proof of Bourgain's Return Times Theorem
- Generalization to systems with purely atomic invariant sigma-algebra
- Enhanced understanding of recurrence properties in dynamical systems

## Abstract

In this diploma thesis (written in German) we present a detailed proof of Bourgain's Return Times Theorem due to Bourgain, Furstenberg, Katznelson and Ornstein following their paper as well as the book by Assani. Moreover, we generalize the result to return time sequences coming from systems with purely atomic invariant $\sigma$-algebra.