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Lebesgue integration. Detailed proofs to be formalized in Coq

Abstract : To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. Sobolev spaces are the mathematical framework in which most weak formulations of partial derivative equations are stated, and where solutions are sought. These functional spaces are built on integration and measure theory. Hence, this chapter in functional analysis is a mandatory theoretical cornerstone for the definition of the finite element method. The purpose of this document is to provide the formal proof community with very detailed pen-and-paper proofs of the main results from integration and measure theory.
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https://hal.inria.fr/hal-03105815
Contributor : Francois Clement <>
Submitted on : Thursday, April 1, 2021 - 6:33:36 PM
Last modification on : Sunday, April 4, 2021 - 3:07:25 AM

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RR-9386.pdf
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  • HAL Id : hal-03105815, version 2
  • ARXIV : 2101.05678

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François Clément, Vincent Martin. Lebesgue integration. Detailed proofs to be formalized in Coq. [Research Report] RR-9386, Inria Paris. 2021, pp.284. ⟨hal-03105815v2⟩

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