Theorems · Theorem · probability
ProbabilityTheory.indepSet_iff_indepSets_singleton
∀ {Ω : Type u_1} {_mΩ : MeasurableSpace Ω} {s t : Set Ω},
MeasurableSet s →
MeasurableSet t →
∀ (μ : autoParam (MeasureTheory.Measure Ω) ProbabilityTheory.indepSet_iff_indepSets_singleton._auto_1)
[MeasureTheory.IsZeroOrProbabilityMeasure μ],
ProbabilityTheory.IndepSet s t μ ↔ ProbabilityTheory.IndepSets {s} {t} μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.diracproof · cited by 210
- ProbabilityTheory.Kernel.constproof · cited by 93
- MeasureTheory.IsZeroOrProbabilityMeasurestatement and proof · cited by 46
- ProbabilityTheory.IndepSetsstatement · cited by 29
- ProbabilityTheory.IndepSetstatement · cited by 13
- ProbabilityTheory.Kernel.indepSet_iff_indepSets_singletonproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.indepSet_iff_measure_inter_eq_mulproof · cited by 0