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

## The Definition of the Riemann Definite Integral and some Related Lemmas

Noboru Endou
Shinshu University, Nagano
Artur Kornilowicz
University of Bialystok
This paper was written while the second author visited Shinshu University, winter 1999.

### Summary.

This article introduces the Riemann definite integral on the closed interval of real. We present the definitions and related lemmas of the closed interval. We formalize the concept of the Riemann definite integral and the division of the closed interval of real, and prove the additivity of the integral.

#### MML Identifier: INTEGRA1

The terminology and notation used in this paper have been introduced in the following articles [26] [7] [29] [2] [27] [14] [4] [30] [16] [15] [20] [24] [10] [12] [3] [25] [21] [8] [28] [17] [18] [23] [9] [11] [19] [22] [1] [6] [13] [5]

#### Contents (PDF format)

1. Definition of Closed Interval and its Properties
2. Definition of Division of Closed Interval and its Properties
3. Definitions of Integrability and Related Topics
4. Real Function's Properties
5. Characteristic Function's Properties
6. Some Properties of Darboux Sum

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