## 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 ℓ^{p}-ball with the ℓ^{q}-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

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