# 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

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topKeiichi 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 -

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## Citations in EuDML Documents

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

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