Show that the set $\Lambda_X := \bigcup_{n \in \mathbb{N}} \left\{y \in \mathbb{R} \mid \mathbb{P}\left(S_n = y\right) > 0\right\}$ is countable and included in $\mathbb{R}^+$.
Show that the set $\Lambda_X := \bigcup_{n \in \mathbb{N}} \left\{y \in \mathbb{R} \mid \mathbb{P}\left(S_n = y\right) > 0\right\}$ is countable and included in $\mathbb{R}^+$.