The Dominated Convergence Theorem in its classical from states: If | X n | Y a.s.,
Question:
Or
Then
Finite.
In the framework of conditional expectations, we have shown that: If |Xn| £ Y a.s., n ³1, εY < 1, εY < ¥, and
With εX finite, then
For any s-field B Ã A.
By means of an example, show that the convergence
Cannot be replaced by
And still conclude that
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Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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