We are going to give necessary and suucient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes .

The purpose of this work is to introduce and study a new topological property called epi-complete-regularity. A space (X, T ) an epi-completely-regular if there exists topology T′ on X which coarser than such that T′) Tychonoff. This investigated some examples are presented in illustrate its relationships with other kinds normality complete-regularity.