Theorems · Theorem · real analysis

variationOnFromTo.rightLim_eq

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_3} [inst_1 : PseudoMetricSpace E] [CompleteSpace E] {f : α → E}
  {a b : α},
  BoundedVariationOn f Set.univ →
    Function.rightLim (variationOnFromTo f Set.univ a) b =
      variationOnFromTo f Set.univ a b + dist (f b) (Function.rightLim f b)

The jump of variationOnFromTo on the right of a point is given by the distance between the right limit and the value of the function.

Defined in

Mathlib.Topology.EMetricSpace.VariationOnFromTo

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoMetricSpaceCompleteSpace