Exact Hausdorff and Packing measure of certain Cantor sets, not necessarily self-similar or homogeneous

TL;DR

This paper calculates the exact Hausdorff and Packing measures of certain linear Cantor sets that are not necessarily self-similar or homogeneous, using the local behavior of the natural probability measure.

Contribution

It provides a method to compute measures of non-self-similar Cantor sets based on their local measure behavior, extending previous results.

Findings

Exact measures for a class of linear Cantor sets.

Method applicable to non-self-similar, non-homogeneous sets.

Advances understanding of measure theory in fractal geometry.

Abstract

We compute the exact Hausdorff and Packing measures of linear Cantor sets which might not be self similar or homogeneous . The calculation is based on the local behavior of the natural probability measure supported on the sets.