| Line 1: | Line 1: | ||
| + | #1 | ||
| + | |||
<math>\int_{\{|f_n|>M\}}|f_n|\leq\int_{(0,1)}|f_n-f|+\int_{\{|f_n|>M\}}|f|</math> | <math>\int_{\{|f_n|>M\}}|f_n|\leq\int_{(0,1)}|f_n-f|+\int_{\{|f_n|>M\}}|f|</math> | ||
| − | <math>Since \int_{(0,1)}|f_n-f|\to0,</math> | + | <math>Since \int_{(0,1)}|f_n-f|\to0(n\to\infinity),</math> |
Revision as of 09:50, 2 July 2008
- 1
$ \int_{\{|f_n|>M\}}|f_n|\leq\int_{(0,1)}|f_n-f|+\int_{\{|f_n|>M\}}|f| $
$ Since \int_{(0,1)}|f_n-f|\to0(n\to\infinity), $
