I am working on the following exercise:
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a $2\pi$ periodic function that is almost everywhere differentiable. (The derivative is a regulated function.) Show that the Fourier series of $f$ converges uniformly on $\mathbb{R}$.
I do not know how I could prove this as the conditions on $f$ are really weak. Could you help me?