Lebesgue-style integration plays a major role in advanced probability. We formalize concepts of elementary measure theory, real-valued random variables as Borel-measurable functions, and a stepwise inductive definition of the integral itself. All proofs are carried out in human readable style using the Isar language.
This article is of historical interest only. Lebesgue-style integration and probability theory are now available as part of the Isabelle/HOL distribution (directory Probability).