  For any nonnegative Borel-measurable function f such that f(x)=0 if and only
if x=0, the best constant c_f in the inequality E f(X-E X) \leq c_f E f(X) for
all random variables X with a finite mean is obtained. Properties of the
constant c_f in the case when f=|.|^p are studied. Applications to
concentration of measure in the form of Rosenthal-type bounds on the moments of
separately Lipschitz functions on product spaces are given.
