Theorems · Definition · measure theory

BoundedContinuousFunction.toLp

{α : Type u_1} →
  {E : Type u_2} →
    {m0 : MeasurableSpace α} →
      (p : ENNReal) →
        (μ : MeasureTheory.Measure α) →
          [inst : TopologicalSpace α] →
            [BorelSpace α] →
              [inst_2 : NormedAddCommGroup E] →
                [SecondCountableTopologyEither α E] →
                  [MeasureTheory.IsFiniteMeasure μ] →
                    (𝕜 : Type u_3) →
                      [inst_5 : Fact (1 ≤ p)] →
                        [inst_6 : NormedRing 𝕜] →
                          [inst_7 : Module 𝕜 E] →
                            [inst_8 : IsBoundedSMul 𝕜 E] → BoundedContinuousFunction α E →L[𝕜] ↥(MeasureTheory.Lp E p μ)

The bounded linear map of considering a bounded continuous function on a finite-measure space as an element of Lp.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

12 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEitherMeasureTheory.IsFiniteMeasureFactNormedRingModuleIsBoundedSMul