On the Differentiability of Measures Which Correspond to Stochastic Processes. I. Processes with Independent Increments

Kolmogorov (see [2] pg. 39) has proved that for each stochastic process there exists a corresponding unique measure on the minimal Borel field containing all cylindrical sets of the space of all functions.
Let $\xi_1(t)$ and $\xi_2(t)$ be processes with independent increments and $\mu_1$ and $\mu_2$ – measures corresponding to these processes. In this paper the conditions for which the measure $\mu_2$ is absolutely continuous with respect to the measure $\mu_1$ are investigated (Theorem A), and the density of the measure $\mu_2$ with respect to the measure $\mu_2$ is calculated (Theorem B).