Theorems · Theorem · measure theory

MeasureTheory.IntegrableOn.of_bound

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] {s : Set α}
  {μ : MeasureTheory.Measure α},
  μ s < ⊤ →
    ∀ {f : α → E},
      MeasureTheory.AEStronglyMeasurable f (μ.restrict s) →
        ∀ (C : ℝ), (∀ᵐ (x : α) ∂μ.restrict s, ‖f x‖ ≤ C) → MeasureTheory.IntegrableOn f s μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

0 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup