Theorems · Theorem · real analysis

variationOnFromTo.eq_left_iff

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
  LocallyBoundedVariationOn f s →
    ∀ {a b c : α},
      a ∈ s → b ∈ s → c ∈ s → (variationOnFromTo f s a b = variationOnFromTo f s a c ↔ variationOnFromTo f s b c = 0)

Defined in

Mathlib.Topology.EMetricSpace.VariationOnFromTo

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpace