Information, Geometry, and Physics Seminar

The theory of Markov categories has recently gained prominence as a framework for general theories of uncertainty, within which one can try to axiomatize probability theory without reference to measure theory. After an introduction to Markov categories together and an overview of existing results, I will explain how to formulate the strong law of large numbers within this framework. This is based on axiomatizing the formation of an empirical distribution from an infinite sequence of samples. I will sketch how to use the law of large numbers as an axiom to derive the de Finetti theorem.