  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.
