Library Lebesgue.Lebesgue_p

This file is part of the Coq Numerical Analysis library
Copyright (C) Boldo, Clément, Martin, Mayero, Mouhcine
This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the COPYING file for more details.

Brief description

Exports support for Lebesgue integration of nonnegative functions.

Description

Additional support for (extended) real numbers

It is based on extended real numbers provided by the Coquelicot library.
See Lebesgue.R_compl, Lebesgue.Rbar_compl, and Lebesgue.sum_Rbar_nonneg.

Support for measurability of subsets and functions

See Lebesgue.sigma_algebra, Lebesgue.sigma_algebra_R_Rbar, and Lebesgue.measurable_fun.

Support for measures

See Lebesgue.measure, Lebesgue.measure_uniq, and Lebesgue.measure_R.

Support for Lebesgue integration of nonnegative measurable functions

See Lebesgue.simple_fun, Lebesgue.Mp, Lebesgue.LInt_p, and Lebesgue.Tonelli.

Usage

This module is meant to be imported after all imports from the Coq standard library, from the Mathematical Components library, and from other external Coq libraries such as Coquelicot and Flocq.
This module may also be used through the import of Lebesgue.Lebesgue_p_wDep, or Lebesgue.Bochner.Bochner_wDep, where it is exported.

From Lebesgue Require Export R_compl Rbar_compl sum_Rbar_nonneg.
From Lebesgue Require Export sigma_algebra sigma_algebra_R_Rbar measurable_fun.
From Lebesgue Require Export measure simple_fun Mp LInt_p Tonelli.
From Lebesgue Require Export measure_uniq measure_R.