Reference from https://www.whitman.edu/documents/Academics/Mathematics/grady.pdf
For a function $f:[a,b] \rightarrow \mathbb{R}$, $V(f,[a,b])=0$ if and only if $f$ is constant on $[a,b]$
If $f\in BV[a,b]$ and $x\in [a,b]$, then the function $g(x)=V(f,[a,x])$ is an increasing function
If $f:[a,b] \rightarrow \mathbb{R}$ is a function of bounded variation then there exist two increasing functions, $f_1$ and $f_2$, such that $f=f_1-f_2$