The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq

The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq

We are concerned with the formalization of measure theory in the Coq proof assistant. Concretely, we extend MathComp-Analysis, a library for functional analysis built on top of the Mathematical Components library, with standard constructions such as charges and the Lebesgue-Stieltjes measure, and wi...

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Veröffentlicht in:Konpyuta Sofutowea 2024/04/23, Vol.41(2), pp.2_41-2_59
Hauptverfasser: Yoshihiro, ISHIGURO, Reynald, AFFELDT
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Functional analysis
Probability theory
Radon
Statistical analysis
Theorems
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description We are concerned with the formalization of measure theory in the Coq proof assistant. Concretely, we extend MathComp-Analysis, a library for functional analysis built on top of the Mathematical Components library, with standard constructions such as charges and the Lebesgue-Stieltjes measure, and with standard theorems such as the Hahn decomposition theorem and the Radon-Nikodým theorem. These are prerequisites for the formalization of probabilistic programs, of probability theory, and also for other applications such as the formalization of connections between derivatives and integrals.
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subjects Functional analysis
Probability theory
Radon
Statistical analysis
Theorems
title The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq
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