Riemann Integral of Functions from ℝ into Real Banach Space
By: Keiko Narita, Noboru Endou and Yasunari Shidama
Open Access
|Jun 2013References
- [1] Grzegorz Bancerek. Cardinal numbers., 1():377-382, 1990.
- [2] Grzegorz Bancerek. The fundamental properties of natural numbers., 1():41-46, 1990.
- [3] Grzegorz Bancerek. The ordinal numbers., 1():91-96, 1990.
- [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1():107-114, 1990.
- [5] Józef Białas. Properties of the intervals of real numbers., 3(): 263-269, 1992.
- [6] Czesław Bylinski. Binary operations., 1():175-180, 1990.
- [7] Czesław Bylinski. The complex numbers., 1():507-513, 1990.
- [8] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets., 1():529-536, 1990.
- [9] Czesław Bylinski. Functions and their basic properties., 1(): 55-65, 1990.
- [10] Czesław Bylinski. Functions from a set to a set., 1():153-164, 1990.
- [11] Czesław Bylinski. Partial functions., 1():357-367, 1990.
- [12] Czesław Bylinski. The sum and product of finite sequences of real numbers., 1():661-668, 1990.
- [13] Czesław Bylinski. Some basic properties of sets., 1():47-53, 1990.
- [14] Agata Darmochwał. Finite sets., 1():165-167, 1990.
- [15] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas., 8():93-102, 1999.
- [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral., 9():191-196, 2001.
- [17] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux’s theorem., 9():197-200, 2001.
- [18] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability forpartial functions from R to R and integrability for continuous functions., 9():281-284, 2001.
- [19] Andrzej Kondracki. Basic properties of rational numbers., 1(): 841-845, 1990.
- [20] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1():273-275, 1990.
- [21] Keiichi Miyajima, Takahiro Kato, and Yasunari Shidama. Riemann integral of functions from R into real normed space., 19():17-22, 2011. doi:10.2478/v10037-011-0003-8.
- [22] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences., 6():265-268, 1997.
- [23] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces., 19():45-49, 2011. doi:10.2478/v10037-011-0008-3.
- [24] Jan Popiołek. Real normed space., 2():111-115, 1991.
- [25] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers., 1():777-780, 1990.
- [26] Yasunari Shidama. Banach space of bounded linear operators., 12():39-48, 2004.
- [27] Andrzej Trybulec. On the sets inhabited by numbers., 11(): 341-347, 2003.
- [28] Michał J. Trybulec. Integers., 1():501-505, 1990.
- [29] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences., 1():569-573, 1990.
- [30] Wojciech A. Trybulec. Vectors in real linear space., 1():291-296, 1990.
- [31] Zinaida Trybulec. Properties of subsets., 1():67-71, 1990.
- [32] Edmund Woronowicz. Relations and their basic properties., 1 ():73-83, 1990.
- [33] Edmund Woronowicz. Relations defined on sets., 1():181-186, 1990.
Language: English
Page range: 145 - 152
Published on: Jun 1, 2013
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
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© 2013 Keiko Narita, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.