Let $\mu$ be a probability measure. Let $\mathcal A$ be a collection of measurable sets and $D(\mathcal A)$ be the minimal $\lambda$-system (Dynkin system) containing $\mathcal A$.

Is $\mu(D)$ for $D\in\mathcal D(\mathcal A)$ determined by $\mu(A)$ for all $A\in \mathcal A$?