Theorems · Theorem · measure theory
Finset.aemeasurable_sum
∀ {M : Type u_2} {ι : Type u_3} {α : Type u_4} [inst : AddCommMonoid M] [inst_1 : MeasurableSpace M] [MeasurableAdd₂ M]
{m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : ι → α → M} (s : Finset ι),
(∀ i ∈ s, AEMeasurable (f i) μ) → AEMeasurable (∑ i ∈ s, f i) μ- Defined in
- Mathlib.MeasureTheory.Group.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidstatement and proof · cited by 12,281
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Finset.sumstatement · cited by 5,195
- Multiset.mapproof · cited by 876
- AEMeasurablestatement and proof · cited by 840
- Finset.valproof · cited by 438
- MeasurableAdd₂statement and proof · cited by 155
- Multiset.mem_mapproof · cited by 72
- Multiset.aemeasurable_sumproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Finset.aemeasurable_fun_sumproof · cited by 5
- ProbabilityTheory.iIndepFun.charFunDual_map_finsetSum_eq_prodproof · cited by 4
- AEMeasurable.tsum'proof · cited by 0