Let $P = (\Omega, \mathcal{F}_{\Omega}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$M = (\Xi, \mathcal{F}_{\Xi})$ is a D1108: Measurable space
(ii)	$X : \Omega \to \Xi$ is a D202: Random variable from $P$ to $M$
(iii)	\begin{equation} \exists \, \xi \in \Xi : \forall \, \omega \in \Omega : X(\omega) = \xi \end{equation}
(iv)	$\sigma_{\text{pullback}} \langle X \rangle$ is a D1730: Pullback sigma-algebra for $X$ on $P$

Then \begin{equation} \sigma_{\text{pullback}} \langle X \rangle = \{ \emptyset, \Omega \} \end{equation}