Theorems · Definition · measure theory
IsPiSystem
{α : Type u_1} → Set (Set α) → PropA π-system is a collection of subsets of α that is closed under binary intersection of
non-disjoint sets. Usually it is also required that the collection is nonempty, but we don't do
that here.
- Defined in
- Mathlib.MeasureTheory.PiSystem
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptyproof · cited by 2,627
Cited by88
Results whose statement or proof uses this declaration.
- MeasurableSpace.induction_on_interstatement and proof · cited by 21
- MeasurableSpace.isPiSystem_measurableSetstatement · cited by 14
- isPiSystem_prodstatement · cited by 11
- ProbabilityTheory.Kernel.IndepSets.indepstatement and proof · cited by 9
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
- isPiSystem_Ixx_memstatement · cited by 5
- ProbabilityTheory.Kernel.indep_iSup_of_directed_leproof · cited by 5
- isPiSystem_Ixxstatement and proof · cited by 4
- MeasureTheory.Measure.FiniteSpanningSetsIn.extstatement and proof · cited by 4
- MeasureTheory.ext_of_generate_finitestatement and proof · cited by 4
- IsPiSystem.prodstatement and proof · cited by 4
- ProbabilityTheory.Kernel.iIndepSets.iIndepstatement and proof · cited by 4