Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains . Formalizing the mathematicalconcept of integration and the associated results in a formal proof assistant helps providing the highest confidence on the correction of numerical programs involving the use of integration, directly or indirectly . We present the Coq formalization of $L^p$~spaces such as Banach spaces . These results are a first milestonetowards the formalization . of the formalized . of . $L$p~ spaces such as . Banach . spaces . The Lebesgueintegral is considered as . perfectly suited for use in mathematical fields such as probability theory, numerical mathematics, and real analysis . It’s considered as perfectly suited to use in . probability theory and . real analysis

Author(s) : Sylvie Boldo, François Clément, Florian Faissole, Vincent Martin, Micaela Mayero

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Keywords : integration - spaces - formalization - suited - numerical -

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