Why we need to show a function is of bounded variation when we are analysing a Fourier series.
For example, we have a function:
\begin{equation*} f(x)=\left\{ \begin{aligned} 8 & , & 0 \leq x \leq \pi, \\ 5 & , & -\pi \leq x <0. \end{aligned} \right. \end{equation*}
I believe BV of this function is 3. So why we need to find this, based on which concepts?
If we find the function is of BV, then how will it help us in further analysis ?
