Journal of Automated Reasoning

, Volume 59, Issue 4, pp 389–423 | Cite as

A Formally Verified Proof of the Central Limit Theorem

Article

Abstract

We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle’s libraries for analysis and measure-theoretic probability. The proof of the theorem uses characteristic functions, which are a kind of Fourier transform, to demonstrate that, under suitable hypotheses, sums of random variables converge weakly to the standard normal distribution. We also discuss the libraries and infrastructure that supported the formalization, and reflect on some of the lessons we have learned from the effort.

Keywords

Interactive theorem proving Measure theory Central limit theorem 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Technische Universität MünchenMunichGermany

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