Startseite Regarding the set-theoretic complexity of the general fractal dimensions and measures maps
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Regarding the set-theoretic complexity of the general fractal dimensions and measures maps

  • Bilel Selmi ORCID logo EMAIL logo und Haythem Zyoudi
Veröffentlicht/Copyright: 2. Oktober 2024
Analysis
Aus der Zeitschrift Analysis Band 45 Heft 1

Abstract

Let ν be a Borel probability measure on d and q , t . This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type

i h - 1 ( q h ( ν ( B ( x i , r i ) ) ) + t g ( r i ) )

for some prescribed functions h and g. The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps.

MSC 2020: 28A78; 28A80

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Received: 2024-09-03
Accepted: 2024-09-13
Published Online: 2024-10-02
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 17.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/anly-2024-0087/html
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