If X:Ω→Ω′X: \Omega \to \Omega ' then we can define X−1:𝒫(Ω′)→𝒫(Ω)X^{-1}: \mathcal{P}(\Omega ') \to \mathcal{P}(\Omega) by X−1(A′)={ω∈Ω:X(ω)∈A′}X^{-1}(A') = \{ \omega \in \Omega : X(\omega) \in A' \} for A′⊂Ω′ A' \subset \Omega '.