Theorems · Theorem · measure theory

BoundedVariationOn.vectorMeasure_Icc

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : DenselyOrdered α] [inst_2 : TopologicalSpace α]
  [inst_3 : OrderTopology α] [inst_4 : SecondCountableTopology α] [inst_5 : CompactIccSpace α] [hα : MeasurableSpace α]
  [inst_6 : BorelSpace α] {E : Type u_2} [inst_7 : NormedAddCommGroup E] [inst_8 : CompleteSpace E] {f : α → E}
  {a b : α} (hf : BoundedVariationOn f Set.univ),
  a ≤ b → hf.vectorMeasure (Set.Icc a b) = Function.rightLim f b - Function.leftLim f a

Defined in

Mathlib.MeasureTheory.VectorMeasure.BoundedVariation

Cited by

6 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderDenselyOrderedTopologicalSpaceOrderTopologySecondCountableTopologyCompactIccSpaceMeasurableSpaceBorelSpaceNormedAddCommGroupCompleteSpace