Nonstandard approach to Hausdorff outer measure

TL;DR

This paper introduces a nonstandard analysis method to precisely determine the Hausdorff outer measure, offering a novel approach to measure theory using Abraham Robinson's techniques.

Contribution

It presents a new nonstandard framework for calculating the exact Hausdorff outer measure, bridging nonstandard analysis with classical measure theory.

Findings

Exact Hausdorff outer measure computed using nonstandard methods

Demonstrates the effectiveness of nonstandard analysis in measure theory

Provides a new perspective on Hausdorff measure calculation

Abstract

We use nonstandard techniques, in the sense of Abraham Robinson, to give the exact Hausdorff outer measure.