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,
nonnegative 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]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Jozef Bialas.
Infimum and supremum of the set of real numbers. Measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [3]
Jozef Bialas.
Series of positive real numbers. Measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [4]
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.
 [6]
Czeslaw Bylinski.
Functions and their basic properties.
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1, 1989.
 [7]
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1, 1989.
 [8]
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 [9]
Beata Padlewska.
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Journal of Formalized Mathematics,
1, 1989.
 [10]
R. Sikorski.
\em Rachunek rozniczkowy i calkowy  funkcje wielu
zmiennych.
Biblioteka Matematyczna. PWN  Warszawa, 1968.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [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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