Theorems · Theorem · measure theory

MeasureTheory.memLp_trim_of_mem_lpMeasSubgroup

∀ {α : Type u_1} {F : Type u_2} {p : ENNReal} [inst : NormedAddCommGroup F] {m m0 : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} (hm : m ≤ m0) (f : ↥(MeasureTheory.Lp F p μ))
  (hf_meas : f ∈ MeasureTheory.lpMeasSubgroup F m p μ), MeasureTheory.MemLp (Exists.choose ⋯) p (μ.trim hm)

If f belongs to lpMeasSubgroup F m p μ, then the measurable function it is almost everywhere equal to (given by AEMeasurable.mk) belongs to ℒp for the measure μ.trim hm.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

2 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup