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2017 | OriginalPaper | Chapter

Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions

Authors : Sergey G. Bobkov, Piotr Nayar, Prasad Tetali

Published in: Geometric Aspects of Functional Analysis

Publisher: Springer International Publishing

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Abstract

We show that, for any metric probability space (M, d, μ) with a subgaussian constant σ ²(μ) and any Borel measurable set A ⊂ M, we have \(\sigma ^{2}(\mu _{A}) \leq c\log \left (e/\mu (A)\right )\sigma ^{2}(\mu )\), where μ _A is a normalized restriction of μ to the set A and c is a universal constant. As a consequence, we deduce concentration inequalities for non-Lipschitz functions.

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Title: Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions
Authors: Sergey G. Bobkov
Piotr Nayar
Prasad Tetali
Publisher: Springer International Publishing
Book: Geometric Aspects of Functional Analysis
Print ISBN: 978-3-319-45281-4

Electronic ISBN: 978-3-319-45282-1

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-45282-1_3

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