Theorems · Definition · measure theory

ContinuousMap.toAEEqFunLinearMap

{α : Type u_1} →
  {γ : Type u_3} →
    [inst : MeasurableSpace α] →
      (μ : MeasureTheory.Measure α) →
        [inst_1 : TopologicalSpace α] →
          [BorelSpace α] →
            {𝕜 : Type u_5} →
              [inst_3 : Semiring 𝕜] →
                [inst_4 : TopologicalSpace γ] →
                  [TopologicalSpace.PseudoMetrizableSpace γ] →
                    [inst_6 : AddCommGroup γ] →
                      [inst_7 : Module 𝕜 γ] →
                        [inst_8 : IsTopologicalAddGroup γ] →
                          [inst_9 : ContinuousConstSMul 𝕜 γ] →
                            [SecondCountableTopologyEither α γ] → C(α, γ) →ₗ[𝕜] α →ₘ[μ] γ

The linear map 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 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceBorelSpaceSemiringTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceAddCommGroupModuleIsTopologicalAddGroupContinuousConstSMulSecondCountableTopologyEither