Theorems · Theorem · measure theory

stronglyMeasurable_of_tendsto

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_5} {m : MeasurableSpace α} [inst : TopologicalSpace β]
  [TopologicalSpace.PseudoMetrizableSpace β] (u : Filter ι) [u.NeBot] [u.IsCountablyGenerated] {f : ι → α → β}
  {g : α → β},
  (∀ (i : ι), MeasureTheory.StronglyMeasurable (f i)) → Filter.Tendsto f u (nhds g) → MeasureTheory.StronglyMeasurable g

A sequential limit of strongly measurable functions is strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

12 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceFilter.NeBotFilter.IsCountablyGenerated