Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Integrability of Bounded Total Functions


Noboru Endou
Shinshu University, Nagano
Katsumi Wasaki
Shinshu University, Nagano
Yasunari Shidama
Shinshu University, Nagano

Summary.

All these results have been obtained by Darboux's theorem in our previous article [10]. In addition, we have proved the first mean value theorem to Riemann integral.

MML Identifier: INTEGRA4

The terminology and notation used in this paper have been introduced in the following articles [21] [24] [1] [22] [12] [3] [8] [25] [2] [15] [16] [6] [14] [13] [20] [19] [17] [23] [7] [9] [11] [18] [5] [4]

Contents (PDF format)

  1. Basic Integrable Functions and First Mean Value Theorem
  2. Integrability of Bounded Total Functions

Bibliography

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[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[7] Czeslaw Bylinski. The sum and product of finite sequences of real numbers. Journal of Formalized Mathematics, 2, 1990.
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[9] Noboru Endou and Artur Kornilowicz. The definition of the Riemann definite integral and some related lemmas. Journal of Formalized Mathematics, 11, 1999.
[10] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Journal of Formalized Mathematics, 11, 1999.
[11] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Journal of Formalized Mathematics, 11, 1999.
[12] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[13] Jaroslaw Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Journal of Formalized Mathematics, 1, 1989.
[14] Jaroslaw Kotowicz. Convergent sequences and the limit of sequences. Journal of Formalized Mathematics, 1, 1989.
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[19] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.
[20] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.
[21] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[22] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[23] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.
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[25] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received February 1, 2000


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