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On the Π0γ-completeness and Σ0γ-completeness of multifractal decomposition sets
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dc.contributor.author | Olsen, Lars Ole Ronnow | |
dc.date.accessioned | 2018-08-03T10:30:05Z | |
dc.date.available | 2018-08-03T10:30:05Z | |
dc.date.issued | 2018 | |
dc.identifier | 252040664 | |
dc.identifier | 78085da0-9412-4c75-acf9-5b25c475c61c | |
dc.identifier | 85044319112 | |
dc.identifier | 000425918600004 | |
dc.identifier.citation | Olsen , L O R 2018 , ' On the Π 0 γ -completeness and Σ 0 γ -completeness of multifractal decomposition sets ' , Mathematika , vol. 64 , no. 1 , pp. 77-114 . https://doi.org/10.1112/S0025579317000365 | en |
dc.identifier.issn | 0025-5793 | |
dc.identifier.other | ORCID: /0000-0002-8353-044X/work/60630694 | |
dc.identifier.uri | https://hdl.handle.net/10023/15762 | |
dc.description.abstract | The purpose of this paper twofold. Firstly, we establish Π0γ-completeness and Σ0γ-completeness of several different classes of multifractal decomposition sets of arbitrary Borel measures (satisfying a mild non-degeneracy condition and two mild “smoothness” conditions). Secondly, we apply these results to study the Π0γ-completeness and Σ0γ-completeness of several multifractal decomposition sets of self-similar measures (satisfying a mild separation condition). For example, a corollary of our results shows if μ is a self-similar measure satisfying the strong separation condition and is not equal to the normalized Hausdorff measure on its support, then the classical multifractal decomposition sets of μ defined by {x ε ℝd | lim r ↘ 0 [log μ(B(x,r))/log r = α]} are Π03-complete provided they are non-empty. | |
dc.format.extent | 38 | |
dc.format.extent | 454961 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematika | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | On the Π0γ-completeness and Σ0γ-completeness of multifractal decomposition sets | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1112/S0025579317000365 | |
dc.description.status | Peer reviewed | en |
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