Theorems · Theorem · measure theory

Asymptotics.IsBigO.integrableAtFilter

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] {f : α → E} {g : α → F} {l : Filter α}
  [inst_1 : MeasurableSpace α] [inst_2 : NormedAddCommGroup F] {μ : MeasureTheory.Measure α} [l.IsMeasurablyGenerated],
  f =O[l] g →
    StronglyMeasurableAtFilter f l μ → MeasureTheory.IntegrableAtFilter g l μ → MeasureTheory.IntegrableAtFilter f l μ

If f = O[l] g on measurably generated l, f is strongly measurable at l, and g is integrable at l, then f is integrable at l.

Defined in

Mathlib.MeasureTheory.Integral.Asymptotics

Cited by

7 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpaceNormedAddCommGroupFilter.IsMeasurablyGenerated