2 problems

Let $\mu$ be a computable measure on $2^{\mathbb N}\times2^{\mathbb N}$, let $\mu_1$ be its first marginal, and let $\mu(\mathord{\cdot}\mid x)$ denote the associated conditional m…

Let $(X,\mu)$ be a computable probability space. Let $T_1,\ldots,T_k$ be computable measure-preserving transformations that commute pairwise. Let $P$ be a $\Pi^0_1$ class with…