measure theory

• January 9th 2007, 04:23 AM
td.math
measure theory
• January 24th 2007, 01:36 PM
Rebesques
What is the sequence (g_n) needed for? :confused:
• June 14th 2007, 02:47 AM
Rebesques
Ok, I think you mean $f_ng_n\rightarrow fg$ in the second one.

For the first one, write

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

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

For the second one, note

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

by part 1, and expand the squares.