Theorems · Theorem · measure theory

MeasureTheory.integrable_norm_rpow_of_le

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  [MeasureTheory.IsFiniteMeasure μ] {f : α → β},
  MeasureTheory.AEStronglyMeasurable f μ →
    ∀ {p q : ℝ},
      0 ≤ p →
        0 ≤ q →
          p ≤ q → MeasureTheory.Integrable (fun x => ‖f x‖ ^ q) μ → MeasureTheory.Integrable (fun x => ‖f x‖ ^ p) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

1 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasureTheory.IsFiniteMeasure