Problem 1436 (difficulty: 7/10)

Let \(\displaystyle f_n :[a,b]\to \R\) be continuous for all \(\displaystyle n\). Prove that \(\displaystyle \{ x: f_n (x)\,\text{convergent}\}\) is a Borel-set, and give a Borel-class as small as possible to which it still belongs.

Give me another random problem!