ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5360 on D6096: Continuous random real number
Probability that a continuous random real number takes value in a countable set is zero
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D6096: Continuous random real number.
Let $B \subseteq \mathbb{R}$ be a D5485: Real set such that
(i) $B$ is a D16: Countable set
Then \begin{equation} \mathbb{P}(X \in B) = 0 \end{equation}