Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

## Bessel's Inequality

Hiroshi Yamazaki
Shinshu University, Nagano
Yasunari Shidama
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

In this article we defined the operation of a set and proved Bessel's inequality. In the first section, we defined the sum of all results of an operation, in which the results are given by taking each element of a set. In the second section, we defined Orthogonal Family and Orthonormal Family. In the last section, we proved some properties of operation of set and Bessel's inequality.

#### MML Identifier: BHSP_5

The terminology and notation used in this paper have been introduced in the following articles                 

#### Contents (PDF format)

1. Sum of the Result of Operation with Each Element of a Set
2. Orthogonal Family and Orthonormal Family
3. Bessel's Inequality

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