| Line 1: | Line 1: | ||
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}</math> are positive, we get the lower bound is 0. This is as good as it get. Examples: | ||
| − | Let <math>\Omega=[0,1]</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 10:56, 22 July 2008
By Fatou's Lemma, we get the upper bound is 1 and since all the functions $ f_{n} $ 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.
