On packing dimension preservation by distribution functions of random variables with independent $\tilde{Q}$-digits

TL;DR

This paper investigates conditions under which distribution functions of certain random variables preserve packing dimension, introducing the concept of faithfulness of packing systems and exploring its relation to dimension preservation.

Contribution

It introduces the notion of faithfulness of fine packing systems for packing dimension calculation and links it to the preservation of packing dimension by distribution functions.

Findings

Established conditions for packing dimension preservation.

Linked faithfulness of packing systems to dimension preservation.

Provided theoretical insights into random variables with independent DIGITS.

Abstract

The article is devoted to finding conditions for the packing dimension preservation by distribution functions of random variables with independent $\tilde{Q}$-digits. The notion of "faithfulness of fine packing systems for packing dimension calculation" is introduced, and connections between this notion and packing dimension preservation are found.