A Proof of the Ergodic Theorem using Nonstandard Analysis

TL;DR

This paper provides a rigorous proof of the Ergodic Theorem utilizing nonstandard analysis, building on previous work by Kamae to offer a novel mathematical approach.

Contribution

It introduces a nonstandard analysis framework to prove the Ergodic Theorem, offering a new perspective and methodology compared to traditional proofs.

Findings

Successful proof of the Ergodic Theorem using nonstandard analysis

Extends Kamae's work with a rigorous nonstandard approach

Provides a foundation for further research in ergodic theory with nonstandard methods

Abstract

The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.