A1 Journal article (refereed)
A note on topological dimension, Hausdorff measure, and rectifiability (2020)

David, G. C., & Le Donne, E. (2020). A note on topological dimension, Hausdorff measure, and rectifiability. Proceedings of the American Mathematical Society, 148(10), 4299-4304. https://doi.org/10.1090/proc/15051

JYU authors or editors

Publication details

All authors or editors: David, Guy C.; Le Donne, Enrico

Journal or series: Proceedings of the American Mathematical Society

ISSN: 0002-9939

eISSN: 1088-6826

Publication year: 2020

Volume: 148

Issue number: 10

Pages range: 4299-4304

Publisher: American Mathematical Society

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1090/proc/15051

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/73974

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1807.02664


We give a sufficient condition for a general compact metric space to admit an n-rectifiable piece, as a consequence of a recent result of David Bate. Let X be a compact metric space of topological dimension n. Suppose that the n-dimensional Hausdorff measure of X, H-n (X), is finite. Suppose further that the lower n-density of the measure H-n is positive, H-n-almost everywhere in X. Then X contains an n-rectifiable subset of positive H-n-measure. Moreover, the assumption on the lower density is unnecessary if one uses recently announced results of Csornyei-Jones.

Keywords: measure theory; complex analysis

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2

Last updated on 2021-07-07 at 21:30