Integral of Non Positive Functions-Reference-Cited by-同舟云学术

Integral of Non Positive Functions

Published:2017-10-01 Issue:3 Volume:25 Page:227-240
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Endou Noboru¹

Affiliation:

1. National Institute of Technology , Gifu College , 2236-2 Kamimakuwa, Motosu, Gifu , Japan

Abstract

Summary In this article, we formalize in the Mizar system [1, 7] the Lebesgue type integral and convergence theorems for non positive functions [8],[2]. Many theorems are based on our previous results [5], [6].

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Reference8 articles.

1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17

2. [2] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.

3. [3] Noboru Endou. Extended real-valued double sequence and its convergence. Formalized Mathematics, 23(3):253–277, 2015. doi:10.1515/forma-2015-0021.10.1515/forma-2015-0021

4. [4] Noboru Endou. Fubini’s theorem on measure. Formalized Mathematics, 25(1):1–29, 2017. doi:10.1515/forma-2017-0001.10.1515/forma-2017-0001

5. [5] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53–70, 2006. doi:10.2478/v10037-006-0008-x.10.2478/v10037-006-0008-x

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