Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.hasSum

∀ {X : Type u_4} {E : Type u_5} {ι : Type u_6} [inst : MeasurableSpace X] [inst_1 : AddCommMonoid E]
  [inst_2 : TopologicalSpace E] [ContinuousAdd E] {L : SummationFilter ι} [L.NeBot] [L.filter.IsCountablyGenerated]
  [TopologicalSpace.PseudoMetrizableSpace E] {f : ι → X → E} {g : X → E},
  (∀ (i : ι), MeasureTheory.StronglyMeasurable (f i)) →
    (∀ (x : X), HasSum (fun i => f i x) (g x) L) → MeasureTheory.StronglyMeasurable g

The infinite sum of strongly measurable functions is measurable, HasSum version.

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

MeasurableSpaceAddCommMonoidTopologicalSpaceContinuousAddSummationFilter.NeBotFilter.IsCountablyGeneratedTopologicalSpace.PseudoMetrizableSpace