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

Sergey Bobkov, Piotr Nayar, Prasad Tetali

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 ${\sigma }^2({\mu }_A)\le c\log \left(e/\mu (A)\right){\sigma }^2(\mu )$, wh…