Completeness property for plans of sequential estimation for Wiener processes with a drift and some uniqueness theorems

The family of $n$-dimensional Wiener processes $x_\lambda(t)=\xi(t)+\lambda t$ is consedered, $\xi(t)$ being the standard Wiener process. Let $\Gamma$ be a “plan”, defined by some closed subset $\Gamma\subset\mathbb R^n\times\mathbb R_+$ and let $\mu_\lambda$ be the corresponding probability measure on $\Gamma$ defined by the first entrance into $\Gamma$. Conditions are given for the plans to posess the completeness property, i. e. for the implication $\int_\Gamma f(x)\,\mu_\lambda(dx)=0\;\forall\lambda\Rightarrow f\equiv0$ to hold.