Absolutely Integrable Functions-Reference-Cited by-同舟云学术

Absolutely Integrable Functions

Published:2022-04-01 Issue:1 Volume:30 Page:31-52
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Endou Noboru¹^ORCID

Affiliation:

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

Abstract

Summary The goal of this article is to clarify the relationship between Riemann’s improper integrals and Lebesgue integrals. In previous articles [6], [7], we treated Riemann’s improper integrals [1], [11] and [4] on arbitrary intervals. Therefore, in this article, we will continue to clarify the relationship between improper integrals and Lebesgue integrals [8], using the Mizar [3], [2] formalism.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Link

https://www.sciendo.com/pdf/10.2478/forma-2022-0004

Reference11 articles.

1. [1] Tom M. Apostol. Mathematical Analysis. Addison-Wesley, 1969.

2. [2] 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:10.1007/978-3-319-20615-817.

3. [3] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.604425130069070

4. [4] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.

5. [5] Noboru Endou. Extended real-valued double sequence and its convergence. Formalized Mathematics, 23(3):253–277, 2015. doi:10.1515/forma-2015-0021.

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