Theorems · Theorem · probability
ProbabilityTheory.iIndepSet.indep_generateFrom_of_disjoint
∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {s : ι → Set Ω},
(∀ (n : ι), MeasurableSet (s n)) →
ProbabilityTheory.iIndepSet s μ →
∀ (S T : Set ι),
Disjoint S T →
ProbabilityTheory.Indep (MeasurableSpace.generateFrom {t | ∃ n ∈ S, s n = t})
(MeasurableSpace.generateFrom {t | ∃ k ∈ T, s k = t}) μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.ofPredstatement · cited by 6,101
- MeasurableSetstatement and proof · cited by 3,075
- Disjointstatement and proof · cited by 2,201
- MeasurableSpace.generateFromstatement · cited by 172
- ProbabilityTheory.Indepstatement · cited by 43
- ProbabilityTheory.iIndepSetstatement and proof · cited by 19
- ProbabilityTheory.Kernel.iIndepSet.indep_generateFrom_of_disjointproof · cited by 4
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