On application of concentration inunctions to estimation of uniform distance between distributions.

In the paper a number of inequalities for uniform distance $\rho$ between different convolutions of $k$-dimentlonal districutions are derived. In particular, we developed an estimates for $\rho (U*W, V*W)$ and $\rho(\prod_{i=1}^nG_i, \exp(\sum_{i=1}^n(G_i-E)))$, where $\exp$ is understanded in sense of convolutions. The generalization of T. V. Arak inequality for concentration functions is obtained.