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A Systematic Study of Multifractal Measures and Dimensions for Image Measures on Moran Sets

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  • Lixin Guo
  • Haythem Zyoudi

Abstract

A central finding of this article is the equivalence between general multifractal Hausdorff and packing measures and their formulation as Henstock–Thomson “variation†measures. Moreover, the equivalence between the above measures for Moran sets under the strong separation condition (SSC) is further established through an application of the density theorem within a general metric space. In addition, ψ⋆ϑ represents the image measure obtained by applying a measurable function ψ to the ergodic Borel probability measure ϑ. We will employ the entropy to determine the expression for the multifractal dimension of the general multifractal measure of ψ⋆ϑ. The last part of the study focuses on the examination of general multifractal measures and their associated dimensions for image measures.MSC2020 Classification: 28A20, 28A75, 28A78, 28A80, 49Q15

Suggested Citation

  • Lixin Guo & Haythem Zyoudi, 2026. "A Systematic Study of Multifractal Measures and Dimensions for Image Measures on Moran Sets," Abstract and Applied Analysis, Hindawi, vol. 2026, pages 1-18, May.
    • Handle: RePEc:hin:jnlaaa:8121274
    DOI: 10.1155/aaa/8121274
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