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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. | ||
| + | |||
| + | Example 1: | ||
| + | <math>f_{n}(x)=1 if x=\frac{1}{n}, 0 otherwise</math> | ||
Revision as of 10:58, 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.
Example 1: $ f_{n}(x)=1 if x=\frac{1}{n}, 0 otherwise $
