Theorems · Theorem · real analysis

BoundedVariationOn.dist_le

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_3} [inst_1 : PseudoMetricSpace E] {f : α → E} {s : Set α},
  BoundedVariationOn f s → ∀ {x y : α}, x ∈ s → y ∈ s → dist (f x) (f y) ≤ (eVariationOn f s).toReal

Defined in

Mathlib.Topology.EMetricSpace.BoundedVariation

Cited by

2 results in Mathlib

Foundations

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

Assumes

LinearOrderPseudoMetricSpace