Randomness on Computable Probability Spaces - A Dynamical Point of View

We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a emph{dynamical} notion of randomness: typicality. Roughly, a point is emph{typical} for some dynamic, if it follows the statistical behavior of the system (Birkhoff\u27s pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every emph{mixing} computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications