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


David, Guy C.; Le Donne, Enrico (2020). A note on topological dimension, Hausdorff measure, and rectifiability. Proceedings of the American Mathematical Society, 148 (10), 4299-4304. DOI: 10.1090/proc/15051


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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

Open Access: Publication channel is not openly available

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


Abstract

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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Last updated on 2020-14-09 at 13:27