Theorems · Definition · measure theory

MeasureTheory.lpMeasToLpTrimLie

{α : Type u_1} →
  (F : Type u_2) →
    (𝕜 : Type u_3) →
      (p : ENNReal) →
        [inst : RCLike 𝕜] →
          [inst_1 : NormedAddCommGroup F] →
            [inst_2 : NormedSpace 𝕜 F] →
              {m m0 : MeasurableSpace α} →
                (μ : MeasureTheory.Measure α) →
                  [inst_3 : Fact (1 ≤ p)] →
                    (hm : m ≤ m0) → ↥(MeasureTheory.lpMeas F 𝕜 m p μ) ≃ₗᵢ[𝕜] ↥(MeasureTheory.Lp F p (μ.trim hm))

lpMeas and Lp F p (μ.trim hm) are isometric, with a linear equivalence.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

4 results in Mathlib

Foundations

Depth 240 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceFact