Riemann Integral of Functions from ℝ into Real Banach Space
Keiko Narita ; Noboru Endou ; Yasunari Shidama
Formalized Mathematics, Tome 21 (2013), p. 145-152 / Harvested from The Polish Digital Mathematics Library
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In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the convergence of sequences. We applied definitions introduced in the previous article [21] to the proof of integrability.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:267180 
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     author = {Keiko Narita and Noboru Endou and Yasunari Shidama},
     title = {Riemann Integral of Functions from $\mathbb{R}$ into Real Banach Space},
     journal = {Formalized Mathematics},
     volume = {21},
     year = {2013},
     pages = {145-152},
     zbl = {1298.26030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0016}
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Keiko Narita; Noboru Endou; Yasunari Shidama. Riemann Integral of Functions from ℝ into Real Banach Space. Formalized Mathematics, Tome 21 (2013) pp. 145-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0016/

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