Theorems · Theorem · measure theory

TopologicalAddGroup.IsSES.integrate_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]
  [inst_10 : BorelSpace A] (μA : MeasureTheory.Measure A) [hμA : μA.IsAddHaarMeasure] [inst_11 : NormedSpace ℝ E]
  [inst_12 : IsTopologicalAddGroup C] [inst_13 : LocallyCompactSpace B] [inst_14 : MeasurableSpace C]
  [inst_15 : BorelSpace C] (μC : MeasureTheory.Measure C) [hμC : μC.IsAddHaarMeasure]
  (f : CompactlySupportedContinuousMap B E), (H.integrate μA μC) f = ∫ (c : C), ((H.pushforward μA) f) c ∂μC

Defined in

Mathlib.MeasureTheory.Measure.Haar.Extension

Cited by

0 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupAddGroupTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupNormedAddCommGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureNormedSpaceIsTopologicalAddGroupLocallyCompactSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasure