We study a class of Borel probability measures, called correlation measures. Our results are of two types: first, we give explicit constructions of non-trivial correlation measures; second, we examine some of the properties of the set of correlation measures. In…

In this paper we improve the rate function in the McDiarmid concentration inequality for separately Lipschitz functions of independent random variables. In particular the rate function tends to infinity at the boundary. We also prove that in some cases the usual…

In this paper we give extensions of the Hoeffding-Azuma inequalities for weighted sums of uniformly bounded martingale differences.