Theorems · Theorem · measure theory

MeasureTheory.tendsto_integral_Iic_zero

∀ {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},
  Filter.Tendsto a l Filter.atBot → Filter.Tendsto (fun i => ∫ (x : ℝ) in Set.Iic (a i), f x ∂μ) l (nhds 0)

Defined in

Mathlib.MeasureTheory.Integral.IntegralEqImproper

Cited by

0 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Filter.IsCountablyGeneratedNormedAddCommGroupNormedSpace