Theorems · Theorem · measure theory

MeasureTheory.Integrable.bdd_smul

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {𝕜 : Type u_8} [inst_1 : NormedRing 𝕜] [inst_2 : Module 𝕜 β] [IsBoundedSMul 𝕜 β] {f : α → β} {φ : α → 𝕜},
  MeasureTheory.Integrable f μ →
    ∀ (C : ℝ), MeasureTheory.AEStronglyMeasurable φ μ → (∀ᵐ (a : α) ∂μ, ‖φ a‖ ≤ C) → MeasureTheory.Integrable (φ • f) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

4 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedRingModuleIsBoundedSMul