Is it true that the continuous $2\pi$-periodic function is almost everywhere differentiable?

Question

Is it true that the continuous $2\pi$-periodic function is almost everywhere differentiable (how to verify this statement)? Is that an absolute continuous function? Could someone provide an explanation for mean of almost everywhere differentiable function. I have not been able to distinghuisd "almost everywhere" and "everywhere" of this context. Thank you.

Answer 1

A continuous periodic function can be nowhere differentiable.

Answer 2

It is not.

The famous counterexample https://en.wikipedia.org/wiki/Weierstrass_function is continuous and periodic, but nowhere differentiable.

A sufficient condition for almost everywhere differentiability (which means differentiability outside of a set of Lebesgue measure zero) is to have bounded variation.