Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Let ν be a Borel probability measure on ℝ d {\mathbb{R}^{d}} and q , t ∈ ℝ {q,t\in\mathbb{R}} . This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type ∑ i h - 1 ( q h ( ν ( B ( x i , r i ) ) ) + t g ( r i ) ) \sum_{i}h^{-1}(qh(\nu(B(x_{i},r_{i})))+tg(r_{i})) for some prescribed functions h and g. The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps.
Let ν be a Borel probability measure on ℝ d {\mathbb{R}^{d}} and q , t ∈ ℝ {q,t\in\mathbb{R}} . This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type ∑ i h - 1 ( q h ( ν ( B ( x i , r i ) ) ) + t g ( r i ) ) \sum_{i}h^{-1}(qh(\nu(B(x_{i},r_{i})))+tg(r_{i})) for some prescribed functions h and g. The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.