Theorems · Theorem · measure theory
MeasurableSpace.isPiSystem_measurableSet
∀ {α : Type u_3} [inst : MeasurableSpace α], IsPiSystem {s | MeasurableSet s}- Defined in
- Mathlib.MeasureTheory.PiSystem
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 64 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.
Cites7
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
- MeasurableSpacestatement and proof · cited by 13,106
- Set.ofPredstatement and proof · cited by 6,101
- MeasurableSetstatement and proof · cited by 3,075
- Set.Nonemptyproof · cited by 2,627
- MeasurableSet.interproof · cited by 167
- IsPiSystemstatement · cited by 88
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.pi_eqproof · cited by 19
- MeasureTheory.Measure.prod_eqproof · cited by 12
- isPiSystem_prodproof · cited by 11
- ProbabilityTheory.Kernel.indep_iSup_of_directed_leproof · cited by 5
- ProbabilityTheory.Kernel.IndepFun.process_indepFunproof · cited by 4
- ProbabilityTheory.Kernel.indep_iSup_of_disjointproof · cited by 3
- MeasureTheory.Integrable.tendsto_ae_condExpproof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- isPiSystem_piproof · cited by 2
- MeasureTheory.MeasurableSet.eq_preimage_restrict_countableproof · cited by 2
- ProbabilityTheory.Kernel.iIndepFun.iIndepFun_processproof · cited by 2
- MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProdproof · cited by 2