Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

Darboux's Theorem


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

Summary.

In this article, we have proved the Darboux's theorem. This theorem is important to prove the Riemann integrability. We can replace an upper bound and a lower bound of a function which is the definition of Riemann integration with convergence of sequence by Darboux's theorem.

MML Identifier: INTEGRA3

The terminology and notation used in this paper have been introduced in the following articles [20] [22] [2] [21] [11] [23] [4] [5] [24] [12] [6] [8] [3] [15] [7] [9] [14] [13] [17] [19] [18] [16] [1] [10]

Contents (PDF format)

  1. Lemmas of Division
  2. Darboux's Theorem

Bibliography

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Received December 7, 1999


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