Theorems · Theorem · measure theory

MeasureTheory.intervalIntegral_tendsto_integral_Iic

∀ {ι : Type u_1} {E : Type u_2} {μ : MeasureTheory.Measure ℝ} {l : Filter ι} [l.IsCountablyGenerated]
  [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a : ι → ℝ} {f : ℝ → E} (b : ℝ),
  MeasureTheory.IntegrableOn f (Set.Iic b) μ →
    Filter.Tendsto a l Filter.atBot →
      Filter.Tendsto (fun i => ∫ (x : ℝ) in a i..b, f x ∂μ) l (nhds (∫ (x : ℝ) in Set.Iic b, f x ∂μ))

Defined in

Mathlib.MeasureTheory.Integral.IntegralEqImproper

Cited by

3 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Filter.IsCountablyGeneratedNormedAddCommGroupNormedSpace