Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989 Association of Mizar Users

## $\sigma$-Fields and Probability

Andrzej Nedzusiak
Warsaw University, Bialystok

### Summary.

This article contains definitions and theorems concerning basic properties of following objects: - a field of subsets of given nonempty set; - a sequence of subsets of given nonempty set; - a $\sigma$-field of subsets of given nonempty set and events from this $\sigma$-field; - a probability i.e. $\sigma$-additive normed measure defined on previously introduced $\sigma$-field; - a $\sigma$-field generated by family of subsets of given set; - family of Borel Sets.

#### MML Identifier: PROB_1

The terminology and notation used in this paper have been introduced in the following articles [8] [4] [11] [10] [12] [2] [3] [1] [9] [6] [5] [7]

Contents (PDF format)

#### Bibliography

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[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Jaroslaw Kotowicz. Convergent sequences and the limit of sequences. Journal of Formalized Mathematics, 1, 1989.
[6] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[7] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[9] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
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[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.