Preprint Concept Paper Version 4 Preserved in Portico This version is not peer-reviewed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)

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

Comments (1)

Comment 1
Received: 17 June 2022
Commenter: Bharath Krishnan
Commenter's Conflict of Interests: Author
Comment: I fixed the title since the original title can be misleading. (I would appreciate if someone stated whether they understand my paper).
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