# Math Help - measure theory

1. ## measure theory

2. What is the sequence (g_n) needed for?

3. 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.