Theorems · Theorem · real analysis

eVariationOn.exists_lt_eVariationOn_inter_Icc

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {ε : ENNReal}
  {s : Set α}, ε < eVariationOn f s → ∃ a ∈ s, ∃ b ∈ s, a < b ∧ ε < eVariationOn f (s ∩ Set.Icc a b)

Defined in

Mathlib.Topology.EMetricSpace.BoundedVariation

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpace