 Generalized fractal dimensions and gauges for self-similar sets and their application in the assessment of coherent conditional previsions and in the calculation of the Sugeno integralRim Achour, Serena Doria, Bilel Selmi and Zhiming Li Chaos, Solitons & Fractals, 2025, vol. 196, issue C Abstract: In this paper, we compute the generalized Hausdorff and packing dimensions of self-similar sets that meet the open set condition. We thoroughly characterize the class of Hausdorff gauges and generalized pre-packing gauges for a self-similar set A that satisfies the open set condition under certain criteria. We derive a more general necessary and sufficient condition for a gauge function to be a Hausdorff gauge for a set A, packing gauge, or pre-packing gauge. Additionally, we estimate the associated Hausdorff measures and packing pre-measures. Finally, we apply these results to assess coherent conditional provisions and to calculate the Sugeno integral with respect to the Lebesgue measure, of the generalized Hausdorff measures of some self-similar sets, such as the middle third Cantor set, the Sierpinsky carpet, and the Sierpinsky triangle. Keywords: Fractal dimensions; Self-similar sets; Sugeno integral; Coherent upper conditional expectation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:196:y:2025:i:c:s096007792500387x DOI: 10.1016/j.chaos.2025.116374 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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