Packing and Hausdorff measures of Cantor sets associated with series

TL;DR

This paper investigates the Hausdorff and packing measures of generalized Cantor sets derived from series, expanding understanding of their geometric measure properties.

Contribution

It introduces a generalized framework for Morán's sum sets and analyzes their Hausdorff and packing measures, providing new insights into their geometric structure.

Findings

Determined conditions for positive Hausdorff measure

Established relationships between series parameters and measure properties

Analyzed measure properties of specific subsets of these Cantor sets

Abstract

We study a generalization of Mor\'an's sum sets, obtaining information about the $h$-Hausdorff and $h$-packing measures of these sets and certain of their subsets.