Computability on random events and variables in a computable probability space

We study aspects of computability concerning random events and variables in a computable probability space which fulfills certain computability axioms. To this end, we introduce two multirepresentations of random events and random variables respectively, employing the Fréchet–Nikodym metric and the Ky Fan metric. They are shown to be recursively complete in guaranteeing computability of basic operations on random events and random variables. Some natural variations of the multirepresentation of random variables are defined for the integrable variables to explore computability of integration.