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dc.contributor.authorNarita, Keiko-
dc.contributor.authorEndou, Noboru-
dc.contributor.authorShidama, Yasunari-
dc.date.accessioned2015-12-09T20:39:48Z-
dc.date.available2015-12-09T20:39:48Z-
dc.date.issued2013-
dc.identifier.citationFormalized Mathematics, Volume 21, Issue 3, 2013, Pages 185-191-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3687-
dc.description.abstractIn 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.-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.subjectformalization of Riemann integral-
dc.titleThe Linearity of Riemann Integral on Functions from R into Real Banach Space-
dc.typeArticle-
dc.identifier.doi10.2478/forma-2013-0020-
dc.description.AffiliationNarita Keiko - Hirosaki-city Aomori, Japan-
dc.description.AffiliationEndou Noboru - Gifu National College of Technology Japan-
dc.description.AffiliationShidama Yasunari - Shinshu University Nagano, Japan-
dc.description.referencesJózef Białas. Properties of the intervals of real numbers. Formalized Mathematics, 3(2): 263-269, 1992.-
dc.description.referencesCzesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.-
dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.-
dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
dc.description.referencesNoboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.-
dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.-
dc.description.referencesKeiichi Miyajima, Takahiro Kato, and Yasunari Shidama. Riemann integral of functions from R into real normed space. Formalized Mathematics, 19(1):17-22, 2011. doi:10.2478/v10037-011-0003-8.-
dc.description.referencesKeiichi Miyajima, Artur Korniłowicz, and Yasunari Shidama. Riemann integral of functions from R into n-dimensional real normed space. Formalized Mathematics, 20(1):79-86, 2012. doi:10.2478/v10037-012-0011-3.-
dc.description.referencesKeiko Narita, Noboru Endou, and Yasunari Shidama. Riemann integral of functions from R into real Banach space. Formalized Mathematics, 21(2):145-152, 2013. doi:10.2478/forma-2013-0016.-
dc.description.referencesAdam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.-
dc.description.referencesHiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011. doi:10.2478/v10037-011-0008-3.-
dc.description.referencesJan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.-
dc.description.referencesKonrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.-
dc.description.referencesYasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.-
dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.-
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.-
dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
dc.description.referencesHiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.-
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