Theorems · Definition · measure theory

ContinuousMap.toAEEqFunAddHom

{α : Type u_1} →
  {β : Type u_2} →
    [inst : MeasurableSpace α] →
      (μ : MeasureTheory.Measure α) →
        [inst_1 : TopologicalSpace α] →
          [BorelSpace α] →
            [inst_3 : TopologicalSpace β] →
              [SecondCountableTopologyEither α β] →
                [TopologicalSpace.PseudoMetrizableSpace β] →
                  [inst_6 : AddGroup β] → [inst_7 : IsTopologicalAddGroup β] → C(α, β) →+ α →ₘ[μ] β

The AddHom from the group of continuous maps from α to β to the group of equivalence classes of μ-almost-everywhere measurable functions.

Defined in

Mathlib.MeasureTheory.Function.AEEqFun

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceBorelSpaceTopologicalSpaceSecondCountableTopologyEitherTopologicalSpace.PseudoMetrizableSpaceAddGroupIsTopologicalAddGroup