Theorems · Theorem · measure theory

TopologicalAddGroup.IsSES.integral_pullback_invFun_apply

∀ {A : Type u_1} {B : Type u_2} {C : Type u_3} {E : Type u_4} [inst : AddGroup A] [inst_1 : AddGroup B]
  [inst_2 : AddGroup C] [inst_3 : TopologicalSpace A] [inst_4 : TopologicalSpace B] [inst_5 : TopologicalSpace C]
  {φ : A →+ B} {ψ : B →+ C} (H : TopologicalAddGroup.IsSES φ ψ) [inst_6 : IsTopologicalAddGroup A]
  [inst_7 : IsTopologicalAddGroup B] [inst_8 : NormedAddCommGroup E] [inst_9 : MeasurableSpace A] [BorelSpace A]
  (μA : MeasureTheory.Measure A) [hμA : μA.IsAddHaarMeasure] [inst_11 : NormedSpace ℝ E]
  (f : CompactlySupportedContinuousMap B E) (b : B),
  ∫ (a : A), (H.pullback f (Function.invFun (⇑ψ) (ψ b))) a ∂μA = ∫ (a : A), (H.pullback f b) a ∂μA

Defined in

Mathlib.MeasureTheory.Measure.Haar.Extension

Cited by

1 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupAddGroupTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupNormedAddCommGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureNormedSpace