A note on topological dimension, Hausdorff measure, and rectifiability
Finna-arvio
A note on topological dimension, Hausdorff measure, and rectifiability
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(Jyväskylän yliopisto - JYX / artikkelit)
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.
Tallennettuna:
Kieli |
englanti |
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Sarja | Proceedings of the American Mathematical Society, 10 |
Aiheet | |
ISSN |
0002-9939 |