Open Access

Riemann Integral of Functions from R into n-dimensional Real Normed Space


Cite

Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Search in Google Scholar

Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Search in Google Scholar

Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Search in Google Scholar

Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Search in Google Scholar

Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Search in Google Scholar

Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Search in Google Scholar

Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Search in Google Scholar

Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Search in Google Scholar

Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Search in Google Scholar

Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.Search in Google Scholar

Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.Search in Google Scholar

Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.Search in Google Scholar

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.Search in Google Scholar

Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.Search in Google Scholar

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/v10037-011-0003-8.10.2478/v10037-011-0003-8Search in Google Scholar

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.10.2478/v10037-009-0021-ySearch in Google Scholar

Keiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.10.2478/v10037-011-0032-3Search in Google Scholar

Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Search in Google Scholar

Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Search in Google Scholar

Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Search in Google Scholar

Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.Search in Google Scholar

Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Search in Google Scholar

Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Search in Google Scholar

Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Search in Google Scholar

Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Search in Google Scholar

Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.Search in Google Scholar

eISSN:
1898-9934
ISSN:
1426-2630
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Computer Sciences, other, Mathematics, General Mathematics