Riemann Integral of Functions from R into Real Normed Space

Keiichi Miyajima; Takahiro Kato; Yasunari Shidama

Formalized Mathematics (2011)

  • Volume: 19, Issue: 1, page 17-22
  • ISSN: 1426-2630

Abstract

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In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].

How to cite

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Keiichi Miyajima, Takahiro Kato, and Yasunari Shidama. "Riemann Integral of Functions from R into Real Normed Space." Formalized Mathematics 19.1 (2011): 17-22. <http://eudml.org/doc/267495>.

@article{KeiichiMiyajima2011,
abstract = {In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].},
author = {Keiichi Miyajima, Takahiro Kato, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {17-22},
title = {Riemann Integral of Functions from R into Real Normed Space},
url = {http://eudml.org/doc/267495},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Keiichi Miyajima
AU - Takahiro Kato
AU - Yasunari Shidama
TI - Riemann Integral of Functions from R into Real Normed Space
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 1
SP - 17
EP - 22
AB - In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].
LA - eng
UR - http://eudml.org/doc/267495
ER -

References

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  16. [16] Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974. 
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Citations in EuDML Documents

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  1. Keiko Narita, Noboru Endou, Yasunari Shidama, Riemann Integral of Functions from ℝ into Real Banach Space
  2. Keiko Narita, Noboru Endou, Yasunari Shidama, The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space
  3. Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, Riemann Integral of Functions from R into n -dimensional Real Normed Space
  4. Keiko Narita, Noboru Endou, Yasunari Shidama, Differential Equations on Functions from R into Real Banach Space
  5. Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, Contracting Mapping on Normed Linear Space

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