Riemann Integral of Functions from R into R n

Keiichi Miyajima; Yasunari Shidama

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 179-185
  • ISSN: 1426-2630

Abstract

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In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].

How to cite

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Keiichi Miyajima, and Yasunari Shidama. " Riemann Integral of Functions from R into R n ." Formalized Mathematics 17.2 (2009): 179-185. <http://eudml.org/doc/267222>.

@article{KeiichiMiyajima2009,
abstract = {In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].},
author = {Keiichi Miyajima, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {179-185},
title = { Riemann Integral of Functions from R into R n },
url = {http://eudml.org/doc/267222},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Keiichi Miyajima
AU - Yasunari Shidama
TI - Riemann Integral of Functions from R into R n
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 179
EP - 185
AB - In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].
LA - eng
UR - http://eudml.org/doc/267222
ER -

References

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Citations in EuDML Documents

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  1. Keiichi Miyajima, Takahiro Kato, Yasunari Shidama, Riemann Integral of Functions R into C
  2. Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, Riemann Integral of Functions from R into n -dimensional Real Normed Space
  3. Keiko Narita, Artur Kornilowicz, Yasunari Shidama, More on the Continuity of Real Functions
  4. Takao Inoué, Noboru Endou, Yasunari Shidama, Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces
  5. Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama, Higher-Order Partial Differentiation
  6. Keiko Narita, Artur Korniłowicz, Yasunari Shidama, The Differentiable Functions from R into R n
  7. Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, Contracting Mapping on Normed Linear Space

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