If $f\_n=1\_{(n,n+1)}(x)$, where $1\_A(x)$ is the indicator function. Why is $f\_n
\rightarrow0$? Same is true for $f\_n=1\_{(n,\infty)}$.


i just dont get it.


i thought $f\_n$ was always 0 for all n so i think $f\_n\rightarrow1$ but its not
the case. i try to reason it by the integral which is 1 for all n
but then i dont go anyway.



strick inequality for Fatou theorem
This is just the definition of convergence for sequences of functions : $\forall x \in \mathbb R, \lim\_{n \to+\infty} f\_n(x) =0$, which is of course the case here, all sequences $(f\_n(x))$ being stationary. 


