Theorems · Theorem · measure theory

TopologicalGroup.IsSES.pushforward_def

∀ {A : Type u_1} {B : Type u_2} {C : Type u_3} {E : Type u_4} [inst : Group A] [inst_1 : Group B] [inst_2 : Group C]
  [inst_3 : TopologicalSpace A] [inst_4 : TopologicalSpace B] [inst_5 : TopologicalSpace C] {φ : A →* B} {ψ : B →* C}
  (H : TopologicalGroup.IsSES φ ψ) [inst_6 : IsTopologicalGroup A] [inst_7 : IsTopologicalGroup B]
  [inst_8 : NormedAddCommGroup E] [inst_9 : MeasurableSpace A] [inst_10 : BorelSpace A] (μA : MeasureTheory.Measure A)
  [hμA : μA.IsHaarMeasure] [inst_11 : NormedSpace ℝ E] [inst_12 : IsTopologicalGroup C]
  [inst_13 : LocallyCompactSpace B] (f : CompactlySupportedContinuousMap B E) (c : C),
  ((H.pushforward μA) f) c = ∫ (a : A), (H.pullback f (Function.invFun (⇑ψ) c)) a ∂μA

Defined in

Mathlib.MeasureTheory.Measure.Haar.Extension

Cited by

0 results in Mathlib

Foundations

Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupGroupTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalGroupIsTopologicalGroupNormedAddCommGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsHaarMeasureNormedSpaceIsTopologicalGroupLocallyCompactSpace