Concept Paper
Version 4
Preserved in Portico This version is not peer-reviewed
Generalizing The Mean From Hausdorff Measure and Fractal-Measures
Version 1
: Received: 2 June 2022 / Approved: 6 June 2022 / Online: 6 June 2022 (08:37:20 CEST)
Version 2 : Received: 6 June 2022 / Approved: 7 June 2022 / Online: 7 June 2022 (08:17:39 CEST)
Version 3 : Received: 9 June 2022 / Approved: 9 June 2022 / Online: 9 June 2022 (09:02:53 CEST)
Version 4 : Received: 16 June 2022 / Approved: 17 June 2022 / Online: 17 June 2022 (08:54:36 CEST)
Version 2 : Received: 6 June 2022 / Approved: 7 June 2022 / Online: 7 June 2022 (08:17:39 CEST)
Version 3 : Received: 9 June 2022 / Approved: 9 June 2022 / Online: 9 June 2022 (09:02:53 CEST)
Version 4 : Received: 16 June 2022 / Approved: 17 June 2022 / Online: 17 June 2022 (08:54:36 CEST)
How to cite: Krishnan, B. Generalizing The Mean From Hausdorff Measure and Fractal-Measures. Preprints 2022, 2022060068. https://doi.org/10.20944/preprints202206.0068.v4 Krishnan, B. Generalizing The Mean From Hausdorff Measure and Fractal-Measures. Preprints 2022, 2022060068. https://doi.org/10.20944/preprints202206.0068.v4
Abstract
I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.
Supplementary and Associated Material
https://www.acadsci.fi/mathematica/Vol38/vol38pp797-804.pdf: GeneralizedHausdorffMeasureOnGenericCompactSets
Keywords
Hausdorff Measure; Fractals; Gauge Function; Dimension Function; Set Theory
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Bharath Krishnan
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