We show that, for any metric probability space (M, d, μ) with a subgaussian constant σ2 (μ) and any Borel measurable set A ⊂ M, we have σ2 (μA) ≤ c log e/μ.(A)) σ2(μ), where μA 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.
|Original language||English (US)|
|Title of host publication||Lecture Notes in Mathematics|
|Number of pages||29|
|State||Published - 2017|
|Name||Lecture Notes in Mathematics|
Bibliographical noteFunding Information:
We would like to thank anonymous referee for pointing out to us several relevant references. S.G. Bobkov’s research supported in part by the Humboldt Foundation, NSF and BSF grants. P. Nayar’s research supported in part by NCN grant DEC-2012/05/B/ST1/00412. P. Tetali’s research supported in part by NSF DMS-1407657.
© Springer International Publishing AG 2017.