Definition of Integrability for Partial Functions from $\Bbb R$ to $\Bbb R$ and Integrability for Continuous Functions

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

Definition of Integrability for Partial Functions from $\Bbb R$ to $\Bbb R$ and Integrability for Continuous Functions

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

Summary.

In this article, we defined the Riemann definite integral of partial function from ${\Bbb R}$ to ${\Bbb R}$. Then we have proved the integrability for the continuous function and differentiable function. Moreover, we have proved an elementary theorem of calculus.

MML Identifier: INTEGRA5

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

Contents (PDF format)

Some Useful Properties of Finite Sequence
Integrability for Partial Function of ${\Bbb R}$, ${\Bbb R}$
Integrability for Continuous Function

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Received March 23, 2000

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