Chu spaces and conditional probability (Q5946862)

The paper recalls the definition of a Chu space and explains the notion of a morphism and an isomorphism between two Chu spaces. Hence, a probability space \((\Omega,P,{\mathcal A})\) is considered and the conditional probability \(P(A|{B})\), where \(A,B\in{\mathcal A}\), is presented as a Chu space. Having two probability spaces \((\Omega,P,{\mathcal A})\), \((\Sigma,Q,{\mathcal B})\) and measurability preserving maps \(\varphi:\Omega\to\Sigma\), \(\psi:\Sigma\to\Omega\), the paper shows an equivalence between \((\psi^{-1},\varphi^{-1})\) being a Chu morphism and \((\varphi,\psi)\) being mutually measure preserving.