Theorems · Theorem · probability
ProbabilityTheory.indepSets_iff_singleton_indepSets
∀ {Ω : Type u_1} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {𝒜 ℬ : Set (Set Ω)},
ProbabilityTheory.IndepSets 𝒜 ℬ μ ↔ ∀ A ∈ 𝒜, ProbabilityTheory.IndepSets {A} ℬ μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.singleton_subset_iffproof · cited by 206
- Set.biUnion_of_singletonproof · cited by 43
- ProbabilityTheory.IndepSetsstatement and proof · cited by 29
- ProbabilityTheory.IndepSets.biUnionproof · cited by 1
- ProbabilityTheory.indepSets_of_indepSets_of_le_leftproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- indepSets_comap_of_bcfproof · cited by 1
- indepSets_comap_pi_of_bcfproof · cited by 1
- indepSets_comap_pi_of_prod_bcfproof · cited by 1
- indepSets_comap_process_of_bcfproof · cited by 1
- indepSets_comap_process_of_prod_bcfproof · cited by 1