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Synthetic probability theory

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If you have a question about this talk, please contact Martin Escardo.

I shall outline an alternative to the standard set-theoretic formulation of probability theory, based on an 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. The approach also gives rise to reasoning principles for the two probabilistically important “equality” relations between random variables: “almost sure equality” and “equality in law”.

This talk is part of the Theoretical computer science seminar series.

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