Hey Tobias!

I was wondering about your entropy paper with John Baez.

Is **FinStat** the opposite category of what Terrence Tao sketches in [this 2010 blog post](https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/)?

> 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}\\)).

(when suitably restricted to finite sets?)

I was wondering about your entropy paper with John Baez.

Is **FinStat** the opposite category of what Terrence Tao sketches in [this 2010 blog post](https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/)?

> 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}\\)).

(when suitably restricted to finite sets?)