Theorems · Definition · measure theory
MeasureTheory.squareCylinders
{ι : Type u_1} → {α : ι → Type u_2} → ((i : ι) → Set (Set (α i))) → Set (Set ((i : ι) → α i))Given a finite set s of indices, a square cylinder is the product of a set S of
∀ i : s, α i and of univ on the other indices. The set S is a product of sets t i such that
for all i : s, t i ∈ C i.
squareCylinders is the set of all such square cylinders.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- Set.piproof · cited by 405
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.IndepFun.process_indepFunproof · cited by 4
- MeasureTheory.generateFrom_squareCylindersstatement and proof · cited by 3
- MeasureTheory.isPiSystem_squareCylindersstatement and proof · cited by 3
- MeasureTheory.MeasurableSet.eq_preimage_restrict_countableproof · cited by 2
- ProbabilityTheory.Kernel.iIndepFun.iIndepFun_processproof · cited by 2
- MeasureTheory.squareCylinders_eq_iUnion_imagestatement · cited by 1