I was going through Egorov's theorem on wikipedia.
It gives a example why should be $\mu(A)<\infty $. Sequence of real valued indicator function is taken. It claims that the sequence: $ f_n(x)=1_{[n,n+1]}(x) $ converges pointwise for $n\in N$ and $x\in\Re$. I am not able to understand how it converges pointwise to $0$ ?