Probability-1 by Albert N. Shiryaev

Probability-1 by Albert N. Shiryaev

Author:Albert N. Shiryaev
Language: eng
Format: epub
Publisher: Springer New York, New York, NY


(52)

and since , we have

(53)

But, by the definition of ρ 1 ×ρ 2,

Hence it follows from (52) and (53) that (50) is valid for .

Now let . The set function

is evidently a σ-finite measure. It is also easily verified that the set function

is a σ-finite measure. As was shown above, λ and v coincide on sets of the form F = A × B, and therefore on the algebra . Hence it follows by Carathéodory’s theorem that λ and v coincide for all .

We turn now to the proof of the full conclusion of Fubini’s theorem. By (47),



Download



Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.