Abstract
We propose an example for which the multifractal Hausdorff and packing measures are mutually singular.
Highlights
Let μ be a probability measure on a metric space X
During the past 25 years there has been an enormous interest in computing the multifractal spectra of measures in the mathematical literature
We notice that the proofs of the multifractal formalism (1.1) in the above-mentioned references are all based on the same key idea
Summary
Let μ be a probability measure on a metric space X. The Hausdorff multifractal spectrum function, fμ, and the packing multifractal spectrum function, Fμ, of the measure μ are defined respectively by fμ(α) = dimH (E(α)) and Fμ(α) = dimP (E(α)) for α ≥ 0, where. During the past 25 years there has been an enormous interest in computing the multifractal spectra of measures in the mathematical literature. The multifractal spectra of various classes of measures in Euclidean space Rn exhibiting some degree of self-similarity have been computed rigorously. We notice that the proofs of the multifractal formalism (1.1) in the above-mentioned references (see for example [3, 9, 13] and references therein) are all based on the same key idea. The measure Hμq,t is a multifractal generalization of the centered Hausdorff measure, whereas Pμq,t is a multifractal generalization of the packing measure. Hausdorff measure and P t denotes the t-dimensional packing measure
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
