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<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 08:50, 2 July 2008
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$ \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), $
