Theorems · Definition · measure theory

MeasureTheory.lpMeasSubgroupToLpTrimIso

{α : Type u_1} →
  (F : Type u_2) →
    (p : ENNReal) →
      [inst : NormedAddCommGroup F] →
        {m m0 : MeasurableSpace α} →
          (μ : MeasureTheory.Measure α) →
            [inst_1 : Fact (1 ≤ p)] →
              (hm : m ≤ m0) → ↥(MeasureTheory.lpMeasSubgroup F m p μ) ≃ᵢ ↥(MeasureTheory.Lp F p (μ.trim hm))

lpMeasSubgroup and Lp F p (μ.trim hm) are isometric.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

0 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupFact