Theorems · Theorem · measure theory

aestronglyMeasurable_of_tendsto_ae

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {ι : Type u_5} [TopologicalSpace.PseudoMetrizableSpace β] (u : Filter ι) [u.NeBot] [u.IsCountablyGenerated]
  {f : ι → α → β} {g : α → β},
  (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ) →
    (∀ᵐ (x : α) ∂μ, Filter.Tendsto (fun n => f n x) u (nhds (g x))) → MeasureTheory.AEStronglyMeasurable g μ

An almost everywhere sequential limit of almost everywhere strongly measurable functions is almost everywhere strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

9 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceFilter.NeBotFilter.IsCountablyGenerated