On conditions of equivalence and perpendicularity of measures corresponding to homogeneous Gaussian fields

Let $t=(t_1,\dots,t_n)\in T\subset\mathbf R^n$, $\mathbf R^n$ be an n-dimensional Euclidean space and let $\xi_1(t)$, $\xi_2(t)$ be homogenous Gaussian fields, $\nu_1$, $\nu_2$ be measures induced by $\xi_1(t)$, $\xi_2(t)$. In the paper, some conditions of equivalence and perpendicularity of $\nu_1$ and $\nu_2$ are obtained.