1. ## Convergence in measure

If $f_{n} \to f$ in measure then prove that |f_n|->|f| in measure.

2. Originally Posted by Chandru1
If $f_{n} \to f$ in measure then prove that |f_n|->|f| in measure.
What does $f_{n} \to f$ in measure mean? That the integrals converge?

3. Originally Posted by southprkfan1
What does $f_{n} \to f$ in measure mean? That the integrals converge?
Nope it means $\mu(|f_n-f|>\epsilon) \rightarrow 0$.

Originally Posted by Chandru1
If $f_{n} \to f$ in measure then prove that |f_n|->|f| in measure.
Have you heard of the reverse triangle inequality? $||x|-|y|| \leq |x-y|$. Use it to prove that $\{||f_n|-|f||> \epsilon\} \subset \{|f_n-f|> \epsilon\}$.