Theorems · Theorem · measure theory

MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_bounded

∀ {ι : Type u_1} {E : Type u_2} {μ : MeasureTheory.Measure ℝ} {l : Filter ι} [l.NeBot] [l.IsCountablyGenerated]
  [inst : NormedAddCommGroup E] {a : ι → ℝ} {f : ℝ → E} (I b : ℝ),
  (∀ (i : ι), MeasureTheory.IntegrableOn f (Set.Ioc (a i) b) μ) →
    Filter.Tendsto a l Filter.atBot →
      (∀ᶠ (i : ι) in l, ∫ (x : ℝ) in a i..b, ‖f x‖ ∂μ ≤ I) → MeasureTheory.IntegrableOn f (Set.Iic b) μ

Defined in

Mathlib.MeasureTheory.Integral.IntegralEqImproper

Cited by

2 results in Mathlib

Foundations

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

Assumes

Filter.NeBotFilter.IsCountablyGeneratedNormedAddCommGroup