Absolutely Integrable Functions

Endou, Noboru

doi:10.2478/forma-2022-0004

Abstract

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.

References

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[4] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.
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[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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[6] Noboru Endou. Improper integral. Part I. Formalized Mathematics, 29(4):201–220, 2021. doi:10.2478/forma-2021-0019.
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[7] Noboru Endou. Improper integral. Part II. Formalized Mathematics, 29(4):279–294, 2021. doi:10.2478/forma-2021-0024.
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[8] Noboru Endou. Relationship between the Riemann and Lebesgue integrals. Formalized Mathematics, 29(4):185–199, 2021. doi:10.2478/forma-2021-0018.
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[9] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491–494, 2001.
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[10] Noboru Endou, Yasunari Shidama, and Masahiko Yamazaki. Integrability and the integral of partial functions from ℝ into ℝ. Formalized Mathematics, 14(4):207–212, 2006. doi:10.2478/v10037-006-0023-y.
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[11] Gerald B. Folland. Real Analysis: Modern Techniques and Their Applications. Wiley, 2nd edition, 1999.
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Absolutely Integrable Functions

Abstract

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