Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.tprod

∀ {X : Type u_4} {E : Type u_5} {ι : Type u_6} [inst : MeasurableSpace X] [inst_1 : CommMonoid E]
  [inst_2 : TopologicalSpace E] [ContinuousMul E] {L : SummationFilter ι} [L.NeBot] [L.filter.IsCountablyGenerated]
  [TopologicalSpace.IsCompletelyPseudoMetrizableSpace E] [Countable ι] {f : ι → X → E},
  (∀ (i : ι), MeasureTheory.StronglyMeasurable (f i)) → MeasureTheory.StronglyMeasurable fun x => ∏'[L] (i : ι), f i x

The infinite product of strongly measurable functions is measurable.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable

Cited by

1 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceCommMonoidTopologicalSpaceContinuousMulSummationFilter.NeBotFilter.IsCountablyGeneratedTopologicalSpace.IsCompletelyPseudoMetrizableSpaceCountable