Theorems · Theorem · probability

ProbabilityTheory.iIndepFun_iff_finset

∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {β : ι → Type u_10}
  {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.iIndepFun f μ ↔ ∀ (s : Finset ι), ProbabilityTheory.iIndepFun (s.restrict f) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites18

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Finsetstatement and proof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Finset.univproof · cited by 3,473
MeasurableSetproof · cited by 3,075
Finset.prodproof · cited by 2,356
Set.extproof · cited by 2,266
Set.iInterproof · cited by 1,084
Subtype.val_injectiveproof · cited by 232

Cited by4

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepFun.restrictproof · cited by 5
ProbabilityTheory.iIndepFun_iff_map_fun_eq_infinitePi_map₀proof · cited by 4
ProbabilityTheory.iIndepFun.map_fun_eq_infinitePi_map₀proof · cited by 3
ProbabilityTheory.HasIndepIncrements.natproof · cited by 2