Poisson type theorems for the number of solutions of random inclusions

Let $F$ be a random mapping of $n$-dimensional space $V^n$ over the finite field $GF(q)$ into $T$-dimensional space $V^T$ over the same field, and $D\subset V^n$, $B\subset V^T$. For systems of inclusions $x\in D$, $F(x)\in B$ sufficient conditions for the weak convergence of the number of solutions to the Poisson type laws as $n,T\to\infty$ are obtained.