Theorems · Theorem · measure theory

MeasureTheory.AECover.integrable_of_integral_bounded_of_nonneg_ae

∀ {α : Type u_1} {ι : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {l : Filter ι} [l.NeBot]
  [l.IsCountablyGenerated] {φ : ι → Set α},
  MeasureTheory.AECover μ l φ →
    ∀ {f : α → ℝ} (I : ℝ),
      (∀ (i : ι), MeasureTheory.IntegrableOn f (φ i) μ) →
        (∀ᵐ (x : α) ∂μ, 0 ≤ f x) → (∀ᶠ (i : ι) in l, ∫ (x : α) in φ i, f x ∂μ ≤ I) → MeasureTheory.Integrable f μ

Defined in

Mathlib.MeasureTheory.Integral.IntegralEqImproper

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceFilter.NeBotFilter.IsCountablyGenerated