I am trying to show that $$f_n(x)=\begin{cases}\frac{1}{n+1}&0\leq x\leq e^n\\0&\text{otherwise}\end{cases}\quad$$ converges almost everywhere, in measure space $ (\mathbb{R}, \mathbb{B(R)}, \mu)$. Any comments will be a great help. Thank you.
I tried considering $\epsilon > 0$, and a positive integer $N$ such that $1/e^n <\epsilon $, but how can I proceed from here. How to conclude it converges almost everywhere. please let me know.