Let $f_n(x) = - \frac{1}{n} \mathbb 1_{[0,n]} (x) $ for $n \in \mathbb N$.
(The 1 should be the indicator function.)
- The sequence converges to $-n-1$, right?
- What about the Lebesgue integral of $f_n$? Can anybody show me if it converges, and if yes, to which value?