Theorems · Definition · measure theory
MeasureTheory.cylinder
{ι : Type u_1} → {α : ι → Type u_2} → (s : Finset ι) → Set ((i : ↥s) → α ↑i) → Set ((i : ι) → α i)Given a finite set s of indices, a cylinder is the preimage of a set S of ∀ i : s, α i by
the projection from ∀ i, α i to ∀ i : s, α i.
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Finsetstatement and proof · cited by 13,712
- Set.preimageproof · cited by 4,946
- Finset.restrictproof · cited by 60
Cited by51
Results whose statement or proof uses this declaration.
- MeasureTheory.measurableCylindersproof · cited by 48
- MeasureTheory.mem_measurableCylindersstatement and proof · cited by 13
- MeasureTheory.closedCompactCylindersproof · cited by 7
- MeasureTheory.Measure.infinitePi_piproof · cited by 6
- MeasureTheory.piContent_cylinderstatement · cited by 5
- MeasureTheory.generateFrom_measurableCylindersproof · cited by 5
- ProbabilityTheory.setBernoulli_ae_subsetproof · cited by 5
- MeasureTheory.mem_closedCompactCylindersstatement and proof · cited by 4
- MeasurableSet.cylinderstatement · cited by 4
- MeasureTheory.compl_mem_measurableCylindersproof · cited by 4
- MeasureTheory.cylinder_emptystatement · cited by 4
- MeasureTheory.cylinder_mem_measurableCylindersstatement and proof · cited by 3