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Slices of Hewitt–Stromberg measures and co-dimensions formula

  • Bilel Selmi ORCID logo EMAIL logo
Veröffentlicht/Copyright: 10. Oktober 2021
Analysis
Aus der Zeitschrift Analysis Band 42 Heft 1

Abstract

This paper studies the behavior of the lower and upper multifractal Hewitt–Stromberg functions under slices onto ( n - m ) -dimensional subspaces. More precisely, we discuss the relationship between the multifractal Hewitt–Stromberg functions of a compactly supported Borel probability measure and those of slices or sections of the measure. In addition, we prove that if μ has a finite m-energy and q lies in a certain somewhat restricted interval, then these functions satisfy the expected adding of co-dimensions formula.

MSC 2010: 28A20; 28A80

Acknowledgements

The author is greatly indebted to Professor Jinjun Li for useful discussions while writing this manuscript and for pointing out that the upper (fractal/multifractal) Hewitt–Stromberg function may not be a metric outer measure. Also, the author would like to thank Professor Lars Olsen for the counterexample.

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Received: 2021-09-12
Accepted: 2021-09-15
Published Online: 2021-10-10
Published in Print: 2022-02-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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