Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform

Masahiko Yamazaki; Hiroshi Yamazaki; Yasunari Shidama

doi:10.2478/v10037-008-0038-7

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Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform

Formalized Mathematics

Volume 16 (2008): Issue 4 (December 2008)

By: Masahiko Yamazaki, Hiroshi Yamazaki and Yasunari Shidama

Open Access

|Mar 2009

Abstract

In this article, we defined a variety of extended Riemann integrals and proved that such integration is linear. Furthermore, we defined the one-sided Laplace transform and proved the linearity of that operator.

MML identifier: INTEGR10, version: 7.9.01 4.101.1015

References

[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
Search in Google Scholar
[2] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
Search in Google Scholar
[3] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
Search in Google Scholar
[4] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
Search in Google Scholar
[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
Search in Google Scholar
[6] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
Search in Google Scholar
[7] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
Search in Google Scholar
[8] Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991.
Search in Google Scholar
[9] Jarosław Kotowicz. One-side limits of a real function at a point. Formalized Mathematics, 2(1):29-40, 1991.
Search in Google Scholar
[10] Yatsuka Nakamura. Half open intervals in real numbers. Formalized Mathematics, 10(1):21-22, 2002.
Search in Google Scholar
[11] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
[12] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Search in Google Scholar
[13] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10037-008-0038-7 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 311 - 317

Published on: Mar 20, 2009

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2009 Masahiko Yamazaki, Hiroshi Yamazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 16 (2008): Issue 4 (December 2008)