Theorems · Theorem · real analysis

variationOnFromTo.abs_le_eVariationOn

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
  BoundedVariationOn f s → ∀ {a b : α}, |variationOnFromTo f s a b| ≤ (eVariationOn f s).toReal

Defined in

Mathlib.Topology.EMetricSpace.VariationOnFromTo

Cited by

0 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpace