Definition:Variation Function

Definition
Let $F : \R \to \R$ be a function that is of bounded variation.

We define the variation function $V_F : \R \to \R$ by:


 * $\map {V_F} x = \map {V_F} {\hointl {-\infty} x}$

for each $x \in \R$, where $\map {V_F} {\hointl {-\infty} x}$ denotes the total variation of $F$ on $\hointl {-\infty} x$.