Theorems · Theorem · measure theory
MeasurableSet.pi
∀ {δ : Type u_4} {X : δ → Type u_6} [inst : (a : δ) → MeasurableSpace (X a)] {s : Set δ} {t : (i : δ) → Set (X i)},
s.Countable → (∀ i ∈ s, MeasurableSet (t i)) → MeasurableSet (s.pi t)- Cited by
- 14 results in Mathlib
- Foundations
- Depth 71 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.
Cites8
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
- MeasurableSetstatement and proof · cited by 3,075
- Set.Countablestatement and proof · cited by 545
- Set.pistatement · cited by 405
- measurable_pi_applyproof · cited by 77
- Set.pi_defproof · cited by 14
- MeasurableSet.biInterproof · cited by 13
Cited by14
Results whose statement or proof uses this declaration.
- MeasurableSet.univ_piproof · cited by 19
- ProbabilityTheory.Kernel.IndepFun.process_indepFunproof · cited by 4
- MeasureTheory.generateFrom_squareCylindersproof · cited by 3
- ZSpan.fundamentalDomain_measurableSetproof · cited by 3
- MeasureTheory.Measure.infinitePi_map_piproof · cited by 2
- NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasisproof · cited by 2
- MeasureTheory.Measure.infinitePi_map_piCurry_symmproof · cited by 2
- ProbabilityTheory.Kernel.iIndepFun.iIndepFun_processproof · cited by 2
- Real.volume_preserving_transvectionStructproof · cited by 1
- MeasureTheory.Measure.infinitePi_map_piCongrLeftproof · cited by 1
- MeasureTheory.Measure.infinitePi_map_restrict'proof · cited by 1
- measurableSet_pi_of_nonemptyproof · cited by 1