Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

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

- 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.

- Definition of Closed Interval and its Properties
- Definition of Division of Closed Interval and its Properties
- Definitions of Integrability and Related Topics
- Real Function's Properties
- Characteristic Function's Properties
- Some Properties of Darboux Sum
- Additivity of Integral

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