I am asked the following question:
By suitable example, show that strict inequality holds in Fatou's lemma
I know that Fatou's lemma states that
Suppose $f_n$ is a sequence of measurable functions with $f_n$ non-negative. If $f_n$ coverges to $f$ for a.e $x$ then $\int f=\liminf\int f_n$.
I need to construct an example to show that strict inequality holds in lemma. Please help. I don't have idea to start.