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
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [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.
 [10]
Andrzej Trybulec and Agata Darmochwal.
Boolean domains.
Journal of Formalized Mathematics,
1, 1989.
 [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.
Received October 16, 1989
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