Theorems · Theorem · real analysis
AbsolutelyContinuousOnInterval.boundedVariationOn
∀ {F : Type u_2} [inst : SeminormedAddCommGroup F] {a b : ℝ} {f : ℝ → F},
AbsolutelyContinuousOnInterval f a b → BoundedVariationOn f (Set.uIcc a b)If f is absolutely continuous on uIcc a b, then f has bounded variation on uIcc a b.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
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Cites80
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by2
Results whose statement or proof uses this declaration.
- AbsolutelyContinuousOnInterval.intervalIntegrable_derivproof · cited by 2
- AbsolutelyContinuousOnInterval.ae_differentiableAtproof · cited by 2