Formalizing Integration Theory with an Application to Probabilistic Algorithms

Inter alia, Lebesgue-style integration plays a major role in advanced probability. We formalize a significant part of its theory in Higher Order Logic using Isabelle/Isar. This involves concepts of elementary measure theory, real-valued random variables as Borel-measurable functions, and a stepwise inductive definition of the integral itself. Building on previous work about formal verification of probabilistic algorithms, we exhibit an example application in this domain; another primitive for randomized functional programming is developed to this end.

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