Wolfram Web Resources. The total variation measure of $\mu$ is defined on $B\in\mathcal{B}$ as:$\abs{\mu}(B) :=\sup\left\{ \sum \norm{\mu(B_i)}_V: \{B_i\}\subset\mathcal{B} \text{ is a countable partition of } B\right\}$where $\norm{\cdot}_V$ denotes the norm of $V$. The total variation of a signed measure µ, on a sigma-ﬁeld A of subsets

Total variation. Roughly speaking, a total variation measure is an infinitesimal version of the absolute value. In classical analysis, the total variation of a function f over an interval [a,b] is deﬁned as v(f,[a,b]):= sup g k i=1 |f (t i)− f (t i−1)|, where the supremum runs over all ﬁnite grids g : a = t 0 < t 1 <...