On the Hewitt Stromberg dimension of product sets

TL;DR

This paper introduces a new class of multifractal measures based on half-open binary cubes to evaluate the Hewitt-Stromberg dimension of product sets, extending classical measure constructions.

Contribution

It develops a novel method for constructing multifractal measures using half-open binary cubes and applies this to analyze the Hewitt-Stromberg dimension of Cartesian products.

Findings

New multifractal measures using binary cubes

Evaluation method for Hewitt-Stromberg dimension of product sets

Extension of measure construction techniques

Abstract

In this paper, we construct new multifractal measures, on the Euclidean space $\mathbb{R}^n$, in a similar manner to Hewitt-Stomberg measures but using the class of all $n$-dimensional half-open binary cubes of covering sets in the definition rather than the class of all balls. As an application we shall be concerned with evaluation of Hewitt-Stromberg dimension of cartesian product sets by means of the dimensions of their components.