Theorems · Theorem · general topology

Measurable.tprod

∀ {X : Type u_6} {E : Type u_7} {ι : Type u_8} [inst : MeasurableSpace X] [inst_1 : CommMonoid E]
  [inst_2 : TopologicalSpace E] [TopologicalSpace.IsCompletelyPseudoMetrizableSpace E] [SecondCountableTopology E]
  [inst_5 : MeasurableSpace E] [BorelSpace E] [MeasurableMul₂ E] [Countable ι] {L : SummationFilter ι} [L.NeBot]
  [L.filter.IsCountablyGenerated] {f : ι → X → E},
  (∀ (i : ι), Measurable (f i)) → Measurable fun x => ∏'[L] (i : ι), f i x

The product of measurable functions is measurable.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.Basic

Cited by

1 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceCommMonoidTopologicalSpaceTopologicalSpace.IsCompletelyPseudoMetrizableSpaceSecondCountableTopologyMeasurableSpaceBorelSpaceMeasurableMul₂CountableSummationFilter.NeBotFilter.IsCountablyGenerated