Hey Tobias!

> We say that one probability space \$$(\Omega',{\mathcal B}', {\mathcal P}')\$$ *extends* another \$$(\Omega,{\mathcal B}, {\mathcal P})\$$ if there is a surjective map \$$\pi: \Omega' \rightarrow \Omega\$$ which is measurable (i.e. \$$\pi^{-1}(E) \in {\mathcal B}'\$$ for every \$$E \in {\mathcal B}\$$) and probability preserving (i.e. \$${\bf P}'(\pi^{-1}(E)) = {\bf P}(E)\$$ for every \$$E \in {\mathcal B}\$$).