Theorems · Definition · probability
MeasureTheory.Filtration.piLE
{ι : Type u_2} →
[inst : Preorder ι] →
{X : ι → Type u_4} → [inst_1 : (i : ι) → MeasurableSpace (X i)] → MeasureTheory.Filtration ι MeasurableSpace.piThe canonical filtration on the product space Π i, X i, where piLE i
consists of measurable sets depending only on coordinates ≤ i.
- Defined in
- Mathlib.Probability.Process.Filtration
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderMeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- Preorderstatement and proof · cited by 7,952
- MeasureTheory.Filtrationstatement · cited by 425
- MeasurableSpace.comapproof · cited by 124
- Preorder.restrictLeproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyMeasurable.dependsOn_of_piLEstatement · cited by 1
- MeasureTheory.Filtration.piLE_eq_comap_frestrictLestatement and proof · cited by 1
- ProbabilityTheory.Kernel.condExp_trajstatement and proof · cited by 1
- Measurable.dependsOn_of_piLEstatement · cited by 0
- ProbabilityTheory.Kernel.condExp_traj'statement and proof · cited by 0