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- Jan 9th 2007, 03:23 AMtd.mathmeasure theory
- Jan 24th 2007, 12:36 PMRebesques
What is the sequence (g_n) needed for? :confused:

- Jun 14th 2007, 01:47 AMRebesques
Ok, I think you mean $\displaystyle f_ng_n\rightarrow fg$ in the second one.

For the first one, write

$\displaystyle f_n^2=(f_n-f+f)^2=(f_n-f)^2+2(f_n-f)f+f^2$

and note that $\displaystyle f_n-f\rightarrow 0$ in measure.

For the second one, note

$\displaystyle (f_n+g_n)^2\rightarrow (f+g)^2$

by part 1, and expand the squares.