Theorems · Theorem · measure theory
isPiSystem_pi
∀ {ι : Type u_1} {α : ι → Type u_2} [inst : (i : ι) → MeasurableSpace (α i)],
IsPiSystem (Set.univ.pi '' Set.univ.pi fun i => {s | MeasurableSet s})Boxes form a π-system.
- Defined in
- Mathlib.MeasureTheory.MeasurableSpace.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.ofPredstatement · cited by 6,101
- Set.imagestatement · cited by 5,609
- Set.univstatement · cited by 3,945
- MeasurableSetstatement · cited by 3,075
- Set.pistatement · cited by 405
- IsPiSystemstatement · cited by 88
- MeasurableSpace.isPiSystem_measurableSetproof · cited by 14
- IsPiSystem.piproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
- MeasureTheory.measurePreserving_arrowProdEquivProdArrowproof · cited by 1