Measure concentration for Euclidean distance in the case of dependent random variables

Let q(n) be a continuous density function in n-dimensional Euclidean space. We think of q(n) as the density function of some random sequence X-n with values in R-n. For I subset of [1. n], let X-I denote the collection of coordinates X-i, i is an element of I, and let X-I, denote the collection of coordinates X-i, i is not an element of I. We denote by Q(I)(x(I)\x(I)) the joint conditional density function of X-I, given X-I. We prove measure concentration for q" in the case when, for an appropriate class of sets I, (i) the conditional densities Q(I) (x(l) \x(I)), as functions of x(I), uniformly satisfy a logarithmic Sobolev inequality and (ii) these conditional densities also satisfy a contractivity condition related to Dobrushin and Shlosman's strong mixing condition.