{
  "id": "1506.06174",
  "version": "v1",
  "published": "2015-06-19T22:44:03.000Z",
  "updated": "2015-06-19T22:44:03.000Z",
  "title": "Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions",
  "authors": [
    "Sergey Bobkov",
    "Piotr Nayar",
    "Prasad Tetali"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that for any metric probability space $(M,d,\\mu)$ with a subgaussian constant $\\sigma^2(\\mu)$ and any set $A \\subset M$ we have $\\sigma^2(\\mu_A) \\leq c \\log\\left(e/\\mu(A)\\right)\\,\\sigma^2(\\mu)$, where $\\mu_A$ is a restriction of $\\mu$ to the set $A$ and $c$ is a universal constant. As a consequence we deduce concentration inequalities for non-Lipschitz functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-19T22:44:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-lipschitz functions",
      "concentration properties",
      "restricted measures",
      "applications",
      "metric probability space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150606174B"
    }
  }
}