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Formalized Haar Measure

Author Floris van Doorn

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Author Details

Floris van Doorn
  • University of Pittsburgh, PA, USA

Funding

This paper is supported by the Sloan Foundation (grant G-2018-10067).

Acknowledgements

I want to thank Jeremy Avigad, Tom Hales, the Leanprover community and the anonymous reviewers for proofreading this paper.

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Floris van Doorn. Formalized Haar Measure. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITP.2021.18

Abstract

We describe the formalization of the existence and uniqueness of the Haar measure in the Lean theorem prover. The Haar measure is an invariant regular measure on locally compact groups, and it has not been formalized in a proof assistant before. We will also discuss the measure theory library in Lean’s mathematical library mathlib, and discuss the construction of product measures and the proof of Fubini’s theorem for the Bochner integral.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Mathematics of computing → Mathematical analysis
Keywords
  • Haar measure
  • measure theory
  • Bochner integral
  • Lean
  • interactive theorem proving
  • formalized mathematics

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