DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedaudited 2026-09-06

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Total-variation function on a compact interval

Definition

If $F : [a, b] \to R$ has bounded variation in the sense of Bounded variation and total variation on an interval, its total-variation function is $V_{F} (x) : = {Var}_{[a, x]} (F), a \leq x \leq b .$ In particular $V_{F} (a) = 0$ ; this agrees with the singleton convention in the cited definition.

Depends on

Bounded variation and total variation on an interval

Used by

Total-variation function of an absolutely continuous function Theorem

Dependency tree · two levels

9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

R. K. Srivastava, MA550 Measure Theory Lecture Notes, §4.11 (standard reference, not scraped)