Definition:Variation Function
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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 $\hointl {-\infty} x$.
Also see
- Results about variation functions can be found here.
Sources
- 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.4$: Functions of Finite Variation