Theorems · Theorem · measure theory
MeasureTheory.generateFrom_squareCylinders
∀ {ι : Type u_2} {α : ι → Type u_1} [inst : (i : ι) → MeasurableSpace (α i)],
MeasurableSpace.generateFrom (MeasureTheory.squareCylinders fun i => {s | MeasurableSet s}) = MeasurableSpace.piThe square cylinders formed from measurable sets generate the product σ-algebra.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 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.
Cites22
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
- MeasurableSpacestatement and proof · cited by 13,106
- SetLike.coeproof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- MeasurableSetstatement and proof · cited by 3,075
- le_antisymmproof · cited by 2,068
- Set.piproof · cited by 405
- iSup_leproof · cited by 190
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.IndepFun.process_indepFunproof · cited by 4
- MeasureTheory.MeasurableSet.eq_preimage_restrict_countableproof · cited by 2
- ProbabilityTheory.Kernel.iIndepFun.iIndepFun_processproof · cited by 2