# Type of convergences

1. Apr 22, 2014

### Funky1981

1. The problem statement, all variables and given/known data

Let fn be a sequence of measurable functions converges to f a.e. Is it possible to get a subsequence fnk of fn s.t. fn converges in L1 ?

2. The attempt at a solution
I have proved the converse statement is true and i guess the above statement is impossible but I fail to prove it.

2. Apr 22, 2014

### jbunniii

Hint: Look for a counterexample where $f_n \rightarrow 0$ pointwise but $\|f_n\| = 1$ for all $n$.

3. Apr 22, 2014

### Funky1981

Thanks for your suggestion