We assume that for all $d \geqslant 0$, $\mathbb{P}(X \in d\mathbb{Z}) < 1$. Show that the set $\Lambda_X$ defined in question 8a is closed under addition and that $r\left(\Lambda_X\right) = 0$.
We assume that for all $d \geqslant 0$, $\mathbb{P}(X \in d\mathbb{Z}) < 1$. Show that the set $\Lambda_X$ defined in question 8a is closed under addition and that $r\left(\Lambda_X\right) = 0$.