Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.tsum

∀ {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.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 sum 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: MeasurableSpace AddCommMonoid TopologicalSpace ContinuousAdd SummationFilter.NeBot Filter.IsCountablyGenerated TopologicalSpace.IsCompletelyPseudoMetrizableSpace Countable

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites31

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Finsetstatement and proof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
AddCommMonoidstatement and proof · cited by 12,281
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
MeasurableSetproof · cited by 3,075
Compl.complproof · cited by 2,925
tsumstatement and proof · cited by 1,148
Summableproof · cited by 778
ContinuousAddstatement and proof · cited by 777

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.AEStronglyMeasurable.tsumproof · cited by 1