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

Definitions and Basic Properties of Measurable Functions


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

Summary.

In this article we introduce some definitions concerning measurable functions and prove related properties.

MML Identifier: MESFUNC1

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

Contents (PDF format)

  1. Cardinal Numbers of ${\Bbb Z}$ and ${\Bbb Q}$
  2. Basic Operations of Extended Real Valued Functions
  3. Level Sets
  4. Measurable Functions

Bibliography

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[6] Jozef Bialas. Series of positive real numbers. Measure theory. Journal of Formalized Mathematics, 2, 1990.
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[15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Journal of Formalized Mathematics, 12, 2000.
[16] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[17] Andrzej Kondracki. Basic properties of rational numbers. Journal of Formalized Mathematics, 2, 1990.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
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[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received September 7, 2000


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