Alex Simpson: Synthetic probability theory

Talk at the Categorical Probability and Statistics workshop 2020: http://perimeterinstitute.ca/personal... Title: Synthetic probability theory Speaker: Alex Simpson Chair: Arthur Parzygnat Date: June 8, 2020 Abstract: I shall outline an alternative to the standard set-theoretic formulation of probability theory, based on a category-theory-influenced axiomatisation of the notion of "random variable" as a primitive concept. The axioms capture desirable properties of random variables, not all of which apply to random variables as usually defined. They are designed to support a streamlined development of probability theory, in which sample spaces play no role and one (almost) never needs to consider sigma-algebras and associated notions of measurability.