Mathlib Map

Theorems · Theorem · probability

ProbabilityTheory.indepSets_piiUnionInter_of_disjoint

∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {s : ι → Set (Set Ω)}
  {S T : Set ι},
  ProbabilityTheory.iIndepSets s μ →
    Disjoint S T → ProbabilityTheory.IndepSets (piiUnionInter s S) (piiUnionInter s T) μ
Defined in
Mathlib.Probability.Independence.Basic
Cited by
0 results in Mathlib
Foundations
Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureDisjoint · cited by 2201DisjointProbabilityTheory.IndepSets · cited by 29ProbabilityTheory.IndepSe…piiUnionInter · cited by 20piiUnionInterProbabilityTheory.iIndepSets · cited by 18ProbabilityTheory.iIndepS…ProbabilityTheory.Kernel.indepSets_piiUnionInter_of_disjoint · cited by 4Kernel.indepSets_piiUnion…ProbabilityTheory.indepSets_p…CITED BYCITES

Cites8

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.