Theorems · Theorem · measure theory

MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] {μ : MeasureTheory.Measure α}
  {f : α → E} {l : Filter α} [l.IsMeasurablyGenerated],
  StronglyMeasurableAtFilter f l μ →
    μ.FiniteAtFilter l →
      ∀ {b : E}, Filter.Tendsto f (l ⊓ MeasureTheory.ae μ) (nhds b) → MeasureTheory.IntegrableAtFilter f l μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupFilter.IsMeasurablyGenerated