Kolmogorov's Zero-One Law
Agnes Doll
Formalized Mathematics, Tome 17 (2009), p. 73-77 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

This article presents the proof of Kolmogorov's zero-one law in probability theory. The independence of a family of σ-fields is defined and basic theorems on it are given.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:267273 
@article{bwmeta1.element.doi-10_2478_v10037-009-0008-8,
     author = {Agnes Doll},
     title = {Kolmogorov's Zero-One Law},
     journal = {Formalized Mathematics},
     volume = {17},
     year = {2009},
     pages = {73-77},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0008-8}
}

Agnes Doll. Kolmogorov's Zero-One Law. Formalized Mathematics, Tome 17 (2009) pp. 73-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0008-8/

[1] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[4] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.

[5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[8] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

[10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

[12] Franz Merkl. Dynkin's lemma in measure theory. Formalized Mathematics, 9(3):591-595, 2001.

[13] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.

[14] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.

[15] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

[16] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.

[17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.

[18] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.

[19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.