Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## Properties of Caratheodor's Measure

Jozef Bialas
University of Lodz

### Summary.

The paper contains definitions and basic properties of Ca\-ra\-the\-o\-dor's 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]. Caratheodor's theorem and some theorems concerning basic properties of Caratheodor's measure are proved. The work is the sixth part of the series of articles concerning the Lebesgue measure theory.

#### MML Identifier: MEASURE4

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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[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
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[10] R. Sikorski. \em Rachunek rozniczkowy i calkowy - funkcje wielu zmiennych. Biblioteka Matematyczna. PWN - Warszawa, 1968.
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[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 June 25, 1992