Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform
Masahiko Yamazaki ; Hiroshi Yamazaki ; Yasunari Shidama
Formalized Mathematics, Tome 16 (2008), p. 311-317 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267480
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     author = {Masahiko Yamazaki and Hiroshi Yamazaki and Yasunari Shidama},
     title = {Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {311-317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0038-7}
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Masahiko Yamazaki; Hiroshi Yamazaki; Yasunari Shidama. Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform. Formalized Mathematics, Tome 16 (2008) pp. 311-317. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0038-7/

[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[2] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[3] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.

[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.

[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

[6] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.

[7] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

[8] Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991.

[9] Jarosław Kotowicz. One-side limits of a real function at a point. Formalized Mathematics, 2(1):29-40, 1991.

[10] Yatsuka Nakamura. Half open intervals in real numbers. Formalized Mathematics, 10(1):21-22, 2002.

[11] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[12] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[13] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.