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

Masahiko Yamazaki; Hiroshi Yamazaki; Yasunari Shidama

Formalized Mathematics (2008)

  • Volume: 16, Issue: 4, page 311-317
  • ISSN: 1426-2630

Abstract

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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

How to cite

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Masahiko Yamazaki, Hiroshi Yamazaki, and Yasunari Shidama. "Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform." Formalized Mathematics 16.4 (2008): 311-317. <http://eudml.org/doc/267480>.

@article{MasahikoYamazaki2008,
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},
author = {Masahiko Yamazaki, Hiroshi Yamazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {311-317},
title = {Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform},
url = {http://eudml.org/doc/267480},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Masahiko Yamazaki
AU - Hiroshi Yamazaki
AU - Yasunari Shidama
TI - Extended Riemann Integral of Functions of Real Variable and One-sided Laplace Transform
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 4
SP - 311
EP - 317
AB - 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
LA - eng
UR - http://eudml.org/doc/267480
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  3. [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. [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. [5] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  6. [6] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  7. [7] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  8. [8] Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991. 
  9. [9] Jarosław Kotowicz. One-side limits of a real function at a point. Formalized Mathematics, 2(1):29-40, 1991. 
  10. [10] Yatsuka Nakamura. Half open intervals in real numbers. Formalized Mathematics, 10(1):21-22, 2002. 
  11. [11] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  12. [12] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  13. [13] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998. 

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