Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992
Association of Mizar Users
Completeness of the $\sigma$-Additive Measure.
Measure Theory
-
Jozef Bialas
-
University of Lodz
Summary.
-
Definitions and basic properties of a $\sigma$-additive,
non-negative measure, with values in $\overline{\Bbb R}$,
the enlarged set of real
numbers, where $\overline{\Bbb R}$ denotes set $\overline{\Bbb R} =
{\Bbb R}\cup\{-\infty,+\infty\}$ - by [10].
The article includes the text being a continuation of the paper
[5].
Some theorems concerning
basic properties of a $\sigma$-additive measure and completeness of the measure
are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[8]
[13]
[12]
[14]
[6]
[7]
[1]
[9]
[2]
[3]
[4]
[5]
Contents (PDF format)
Bibliography
- [1]
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Journal of Formalized Mathematics,
1, 1989.
- [2]
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2, 1990.
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Jozef Bialas.
Series of positive real numbers. Measure theory.
Journal of Formalized Mathematics,
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Jozef Bialas.
The $\sigma$-additive measure theory.
Journal of Formalized Mathematics,
2, 1990.
- [5]
Jozef Bialas.
Several properties of the $\sigma$-additive measure.
Journal of Formalized Mathematics,
3, 1991.
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1, 1989.
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\em Rachunek rozniczkowy i calkowy - funkcje wielu
zmiennych.
Biblioteka Matematyczna. PWN - Warszawa, 1968.
- [11]
Andrzej Trybulec.
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Axiomatics, 1989.
- [12]
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Journal of Formalized Mathematics,
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- [13]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [14]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received February 22, 1992
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