Total variation of a function
= Total variation of a function
{title2=$V_a^b(f)$}
{wiki=Total_variation}
The total variation of $f:[a,b]\to\mathbb R$ is
$$
V_a^b(f)=\sup_{a=t_0<\cdots<t_n=b}
\sum_{k=1}^n|f(t_k)-f(t_{k-1})|.
$$
The function has bounded variation when this quantity is finite.