Abstract
In this paper, we study the Levy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional ℓp-ball with the ℓq-distance function for 1 ≤ p≤ q ≤ +∞ is equivalent to the concentration to the real line.
Original language | English |
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Pages (from-to) | 2407-2417 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 137 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2009 Jul |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics