Theorems · Theorem · measure theory

MeasureTheory.Integrable.bdd_mul

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {𝕜 : Type u_8} [inst : NormedRing 𝕜]
  {f g : α → 𝕜} {c : ℝ},
  MeasureTheory.Integrable g μ →
    MeasureTheory.AEStronglyMeasurable f μ →
      (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ c) → MeasureTheory.Integrable (fun x => f x * g x) μ

Defined in: Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by: 1 results in Mathlib
Foundations: Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedRing

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Norm.normstatement and proof · cited by 5,413
Filter.Eventuallystatement and proof · cited by 3,134
MeasureTheory.aestatement and proof · cited by 2,352
MeasureTheory.Integrablestatement and proof · cited by 1,367
NormedRingstatement and proof · cited by 924
MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
MeasureTheory.Integrable.bdd_smulproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.IntegrableOn.continuousOn_mul_of_subsetproof · cited by 2