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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
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Online
ISSN
1898-9934
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Volume 21, Issue 3 (Oct 2013)

Issues

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

Keiko Narita
  • Hirosaki-city Aomori, Japan
/ Noboru Endou
  • Gifu National College of Technology Japan
/ Yasunari Shidama
  • Shinshu University Nagano, Japan

Summary

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.

Keywords: formalization of Riemann integral

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About the article

Published in Print: 2013-10-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0020. Export Citation

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