Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

## Dynkin's Lemma in Measure Theory

Franz Merkl
University of Bielefeld

### Summary.

This article formalizes the proof of Dynkin's lemma in measure theory. Dynkin's lemma is a useful tool in measure theory and probability theory: it helps frequently to generalize a statement about all elements of a intersection-stable set system to all elements of the sigma-field generated by that system.

#### MML Identifier: DYNKIN

The terminology and notation used in this paper have been introduced in the following articles [11] [3] [13] [5] [12] [9] [14] [1] [2] [4] [10] [6] [7] [8]

#### Contents (PDF format)

1. Preliminaries
2. Disjoint-valued Functions and Intersection
3. Dynkin Systems: Definition and Closure Properties
4. Main Steps for Dynkin's Lemma

#### Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[5] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[6] Michal Muzalewski and Leslaw W. Szczerba. Construction of finite sequence over ring and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.
[7] Andrzej Nedzusiak. $\sigma$-fields and probability. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Nedzusiak. Probability. Journal of Formalized Mathematics, 2, 1990.
[9] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[10] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[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.