Theorems · Theorem · real analysis

eVariationOn.union

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) {s t : Set α}
  {x : α}, IsGreatest s x → IsLeast t x → eVariationOn f (s ∪ t) = eVariationOn f s + eVariationOn f t

If a set s is to the left of a set t, and both contain the boundary point x, then the variation of f along s ∪ t is the sum of the variations.

Defined in

Mathlib.Topology.EMetricSpace.BoundedVariation

Cited by

4 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpace