Random rational number

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
Let $M = (\mathbb{Q}, \mathcal{B}(\mathbb{Q}))$ be the D5264: Standard rational borel measurable space.
A D4364: Real function $X : \Omega \to \mathbb{Q}$ is a random rational number on $P$ if and only if $$\forall \, E \in \mathcal{B}(\mathbb{Q}) : X^{-1}(E) \in \mathcal{F}$$

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
Let $M = (\mathbb{Q}, \mathcal{B}(\mathbb{Q}))$ be the D5264: Standard rational borel measurable space.
A D4364: Real function $X : \Omega \to \mathbb{Q}$ is a random rational number on $P$ if and only if $$\forall \, E \in \mathcal{B}(\mathbb{Q}) : \{ X \in E \} \in \mathcal{F}$$

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
Let $M = (\mathbb{Q}, \mathcal{B}(\mathbb{Q}))$ be the D5264: Standard rational borel measurable space.
A D4364: Real function $X : \Omega \to \mathbb{Q}$ is a random rational number on $P$ if and only if $$\sigma_{\text{pullback}, M} \langle X \rangle \subseteq \mathcal{F}$$