Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lipschitz representations of subsets of the cube


Author: Shahar Mendelson
Journal: Proc. Amer. Math. Soc. 135 (2007), 1455-1463
MSC (2000): Primary 46B07, 60D05
Published electronically: November 14, 2006
MathSciNet review: 2276655
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that for any class of uniformly bounded functions $ H$ with a reasonable combinatorial dimension, the vast majority of small subsets of the $ n$-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of $ H$, unless the Lipschitz constant is very large. We apply this result to the case when $ H$ consists of linear functionals of norm at most one on a Hilbert space.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B07, 60D05

Retrieve articles in all journals with MSC (2000): 46B07, 60D05


Additional Information

Shahar Mendelson
Affiliation: Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia
Email: shahar.mendelson@anu.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08620-5
PII: S 0002-9939(06)08620-5
Received by editor(s): April 29, 2005
Received by editor(s) in revised form: December 20, 2005
Published electronically: November 14, 2006
Additional Notes: The author was supported in part by an Australian Research council Discovery grant.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.