The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

Keiko Narita; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2013)

  • Volume: 21, Issue: 3, page 185-191
  • ISSN: 1426-2630

Abstract

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In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

How to cite

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Keiko Narita, Noboru Endou, and Yasunari Shidama. "The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space." Formalized Mathematics 21.3 (2013): 185-191. <http://eudml.org/doc/266690>.

@article{KeikoNarita2013,
abstract = {In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.},
author = {Keiko Narita, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {formalization of Riemann integral},
language = {eng},
number = {3},
pages = {185-191},
title = {The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space},
url = {http://eudml.org/doc/266690},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Keiko Narita
AU - Noboru Endou
AU - Yasunari Shidama
TI - The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 3
SP - 185
EP - 191
AB - In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.
LA - eng
KW - formalization of Riemann integral
UR - http://eudml.org/doc/266690
ER -

References

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