A doubling subset of $L_p$ for $p>2$ that is inherently infinite dimensional
Abstract
It is shown that for every $p\in (2,\infty)$ there exists a doubling subset of $L_p$ that does not admit a bi-Lipschitz embedding into $\R^k$ for any $k\in \N$.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2013
- DOI:
- 10.48550/arXiv.1308.4554
- arXiv:
- arXiv:1308.4554
- Bibcode:
- 2013arXiv1308.4554L
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Functional Analysis