Let $B \in \mathcal{R}$ and $N(\mu,1)(B)$ a free event, wich means it doesn't depends on the unknown parameter $\mu$. Then prove that $B$ or $B^c$ is $N(\mu,1)$-null.
I've alredy proven that if the statistic structure is complete, then the only free events are P-null or complementary. A complete statistic structure is the one that every centered($E_\mu T =0$) real statistic is P-equivalent to zero, i.e. $P_\mu (T^{-1}(\{0\}))=1$.
