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2012 | 20 | 1 | 79-86
Tytuł artykułu

Riemann Integral of Functions from R inton-dimensional Real Normed Space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
1
Strony
79-86
Opis fizyczny
Daty
wydano
2012-01-01
online
2012-09-12
Twórcy
  • Faculty of Engineering, Ibaraki University, Hitachi, Japan
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok Poland
  • Shinshu University, Nagano, Japan
Bibliografia
  • Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
  • Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
  • Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.
  • Noboru 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.
  • Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.
  • Keiichi 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.[Crossref]
  • Keiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.[Crossref]
  • Keiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.[Crossref]
  • Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.
  • Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0011-3
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