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| − | By Fatou's Lemma, we get the upper bound is 1 and since all the functions <math>f_{n}</math> are positive, we get the lower bound is 0. This is as good as it get. Examples: | + | By Fatou's Lemma, we get the upper bound is 1 and since all the functions <math>f_{n}\frac{}{}</math> are positive, we get the lower bound is 0. This is as good as it get. Examples: |
Let <math>\Omega=[0,1]\frac{}{}</math>, the <math>\sigma-</math>algebra is the power set and counting measure. | Let <math>\Omega=[0,1]\frac{}{}</math>, the <math>\sigma-</math>algebra is the power set and counting measure. | ||
Revision as of 09:57, 22 July 2008
By Fatou's Lemma, we get the upper bound is 1 and since all the functions $ f_{n}\frac{}{} $ are positive, we get the lower bound is 0. This is as good as it get. Examples:
Let $ \Omega=[0,1]\frac{}{} $, the $ \sigma- $algebra is the power set and counting measure.
