Talk:Monotone class theorem

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Made the page. --Steffen Grønneberg 14:16, 12 April 2006 (UTC)[reply]

how about a proof?

and the fact that it also coincides with sigma-ring?

Another two Monotone Class Theorems?

1st: In Durret's book (1995), (1.4) of chapter 5. It involves a vector space of real valued functions on big omega.

2nd: <a href="http://www.math.cmu.edu/~gbrunick/mct.pdf">Here</a> is another version.Jackzhp 17:42, 8 April 2007 (UTC)[reply]

Definition of Monotone Class

The definition of a monotone class in the first reference (Probability Essentials by Jacod and Protter) is different from the one given in this article. Namely, in the book a monotone class is closed under monotone ( increasing) limits, and also under differences. Even if the two definitions are equivalent, this makes some parts of the proof "not so plain" to verify. I'm specifically referring to the part concerning the fact that ${\mathcal {B}}_{B}$ is closed under differences. --Trefoilknot (talk) 19:18, 24 February 2014 (UTC)[reply]

This is true and should be corrected. It seems that what Jacod and Protter call a monotone class is what is usually called a Dynkin class or a Dynkin system. A Dynkin system is not, in general, the same as a monotone class. The proof found in the article is actually the proof of what is usually called Dynkin's Lemma. The two are related, but not the same. Isdatmaths (talk) 13:39, 3 July 2014 (UTC)[reply]