Theorems · Theorem · measure theory

BoundedVariationOn.vectorMeasure_Iic

∀ {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.Iic a) = Function.rightLim f a - Filter.atBot.limUnder f

Defined in: Mathlib.MeasureTheory.VectorMeasure.BoundedVariation
Cited by: 1 results in Mathlib
Foundations: Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder DenselyOrdered TopologicalSpace OrderTopology SecondCountableTopology CompactIccSpace MeasurableSpace BorelSpace NormedAddCommGroup CompleteSpace

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
LinearOrderstatement and proof · cited by 8,572
nhdsproof · cited by 5,554
Set.univstatement and proof · cited by 3,945
Filter.Tendstoproof · cited by 3,814
Filter.Eventuallyproof · cited by 3,134
CompleteSpacestatement and proof · cited by 2,532
Set.iUnionproof · cited by 2,483

Cited by1

Results whose statement or proof uses this declaration.

BoundedVariationOn.vectorMeasure_Iioproof · cited by 1