Theorems · Theorem · probability
MeasureTheory.Filtration.filtrationOfSet_eq_natural
∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} {β : ι → Type u_3} [inst : (i : ι) → TopologicalSpace (β i)]
[inst_1 : ∀ (i : ι), TopologicalSpace.MetrizableSpace (β i)] [mβ : (i : ι) → MeasurableSpace (β i)]
[inst_2 : ∀ (i : ι), BorelSpace (β i)] [inst_3 : Preorder ι] [inst_4 : (i : ι) → MulZeroOneClass (β i)]
[∀ (i : ι), Nontrivial (β i)] {s : ι → Set Ω} (hsm : ∀ (i : ι), MeasurableSet (s i)),
MeasureTheory.filtrationOfSet hsm = MeasureTheory.Filtration.natural (fun i => (s i).indicator fun x => 1) ⋯- Defined in
- Mathlib.Probability.Process.Filtration
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- MeasurableSetstatement and proof · cited by 3,075
- Compl.complproof · cited by 2,925
- Nontrivialstatement and proof · cited by 2,416
- iSupproof · cited by 2,415
- Set.extproof · cited by 2,266
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eqproof · cited by 1