On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes

In the paper, conditions are studied under which the measures corresponding to Wiener processes with different drifts are equivalent. The main theorem assepts that, if the drift coefficient (measurable with respect to the past of the observation process) is square integrable a.s. at both «observation-process» and «Wiener-process point», then the measures of the process are equivalent.
The result is applied to the existence and uniqueness of a weak of the stochastic equation $d\xi=\gamma(t,\xi)\,dt+dW$.