Theorems · Theorem · measure theory

MeasureTheory.AECover.lintegral_tendsto_of_nat

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {φ : ℕ → Set α},
  MeasureTheory.AECover μ Filter.atTop φ →
    ∀ {f : α → ENNReal},
      AEMeasurable f μ → Filter.Tendsto (fun x => ∫⁻ (x : α) in φ x, f x ∂μ) Filter.atTop (nhds (∫⁻ (x : α), f x ∂μ))

Defined in: Mathlib.MeasureTheory.Integral.IntegralEqImproper
Cited by: 1 results in Mathlib
Foundations: Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
nhdsstatement and proof · cited by 5,554
Filter.Tendstostatement and proof · cited by 3,814
Set.iUnionproof · cited by 2,483
Filter.atTopstatement and proof · cited by 2,405
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
MeasureTheory.lintegralstatement and proof · cited by 1,152
Set.Iicproof · cited by 1,111
Set.iInterproof · cited by 1,084

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.AECover.lintegral_tendsto_of_countably_generatedproof · cited by 3