On packing dimension preservation by distribution functions of random variables with independent <math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mrow><mi mathvariant="italic">Q</mi></mrow><mo stretchy="false">˜</mo></mover></math>-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.

Keywords

• Packing dimension of a set
• Hausdorff–Besicovitch dimension of a set
• faithfulness of fine packing system for packing dimension calculation
• Q̃-expansion of real numbers
• packing-dimension-preserving transformations