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.
@article{bwmeta1.element.doi-10_2478_forma-2013-0020,
author = {Keiko Narita and Noboru Endou and Yasunari Shidama},
title = {The Linearity of Riemann Integral on Functions from $\mathbb{R}$ into Real Banach Space},
journal = {Formalized Mathematics},
volume = {21},
year = {2013},
pages = {185-191},
zbl = {1298.26031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0020}
}
Keiko Narita; Noboru Endou; Yasunari Shidama. The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space. Formalized Mathematics, Tome 21 (2013) pp. 185-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0020/
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