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

## Scalar Multiple of Riemann Definite Integral

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

### Summary.

The goal of this article is to prove a scalar multiplicity of Riemann definite integral. Therefore, we defined a scalar product to the subset of real space, and we proved some relating lemmas. At last, we proved a scalar multiplicity of Riemann definite integral. As a result, a linearity of Riemann definite integral was proven by unifying the previous article [11].

#### MML Identifier: INTEGRA2

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

#### Contents (PDF format)

1. Lemmas of Finite Sequence
2. Scalar Product of Real Subset
3. Scalar Multiple of Integral
4. Monotoneity of Integral
5. Definition of Division Sequence

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