Can you please give an example of a function with an infinite number of maxima and minima occurring in any finite time interval?
Edit: This question came to me as I was reading on the dirichlet conditions for the fourier transform of a function $g(t)$ to exist. Given that $g(t)$ is a non-periodic and deterministic signal, one of the conditions is that $g(t)$ be a single-valued function, with a finite number of maxima and minima in any finite time interval. Hence the question.
Let $\chi_{\Bbb Q}(x):=1 $ if $x \in \Bbb Q$ and $0$ otherwise.