Theorems · Theorem · measure theory

MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim

∀ {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.trim hm))),
  MeasureTheory.MemLp.toLp ↑↑f ⋯ ∈ MeasureTheory.lpMeasSubgroup F m p μ

If f belongs to Lp for the measure μ.trim hm, then it belongs to the subgroup lpMeasSubgroup F m p μ.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroup