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.
CITATION STYLE
Bobkov, S. G., Nayar, P., & Tetali, P. (2017). Concentration properties of restricted measures with applications to non-Lipschitz functions. In Lecture Notes in Mathematics (Vol. 2169, pp. 25–53). Springer Verlag. https://doi.org/10.1007/978-3-319-45282-1_3
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