A note on topological dimension, Hausdorff measure, and rectifiability
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
Published inProceedings of the American Mathematical Society
DisciplineMatematiikkaGeometrinen analyysi ja matemaattinen fysiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsGeometric Analysis and Mathematical PhysicsAnalysis and Dynamics Research (Centre of Excellence)
© 2020 American Mathematical Society
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.
PublisherAmerican Mathematical Society
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Research post as Academy Research Fellow, AoF; Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.