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.

MML Identifier: MEASURE3

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

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[3] Jozef Bialas. Series of positive real numbers. Measure theory. Journal of Formalized Mathematics, 2, 1990.
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[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Beata Padlewska. Families of sets. 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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