Theorems · Definition · measure theory

TopologicalAddGroup.IsSES.pushforward

{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} →
                        TopologicalAddGroup.IsSES φ ψ →
                          [IsTopologicalAddGroup A] →
                            [IsTopologicalAddGroup B] →
                              [inst_8 : NormedAddCommGroup E] →
                                [inst_9 : MeasurableSpace A] →
                                  [BorelSpace A] →
                                    (μA : MeasureTheory.Measure A) →
                                      [hμA : μA.IsAddHaarMeasure] →
                                        [inst : NormedSpace ℝ E] →
                                          [IsTopologicalAddGroup C] →
                                            [LocallyCompactSpace B] →
                                              CompactlySupportedContinuousMap B E →ₗ[ℝ]
                                                CompactlySupportedContinuousMap C E

If φ : A →+ B and ψ : B →+ C define a short exact sequence of additive topological groups, then we can push forward a continuous compactly supported function on B to a continuous compactly supported function on C by integrating over A.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Extension

Cited by

6 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupAddGroupTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupNormedAddCommGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureNormedSpaceIsTopologicalAddGroupLocallyCompactSpace