Theorems · Theorem · measure theory

BoundedVariationOn.vectorMeasure_Ici

∀ {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}
  (hf : BoundedVariationOn f Set.univ) (a : α),
  hf.vectorMeasure (Set.Ici a) = Filter.atTop.limUnder f - Function.leftLim f a

Defined in

Mathlib.MeasureTheory.VectorMeasure.BoundedVariation

Cited by

2 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderDenselyOrderedTopologicalSpaceOrderTopologySecondCountableTopologyCompactIccSpaceMeasurableSpaceBorelSpaceNormedAddCommGroupCompleteSpace