Theorems · Theorem · real analysis

hasConstantSpeedOnWith_iff_variationOnFromTo_eq

∀ {E : Type u_2} [inst : PseudoEMetricSpace E] {f : ℝ → E} {s : Set ℝ} {l : NNReal},
  HasConstantSpeedOnWith f s l ↔
    LocallyBoundedVariationOn f s ∧ ∀ ⦃x : ℝ⦄, x ∈ s → ∀ ⦃y : ℝ⦄, y ∈ s → variationOnFromTo f s x y = ↑l * (y - x)

Defined in: Mathlib.Analysis.ConstantSpeed
Cited by: 1 results in Mathlib
Foundations: Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoEMetricSpace

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Cited by1

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HasConstantSpeedOnWith.ratioproof · cited by 1