Theorems · Theorem · probability
ProbabilityTheory.indepSet_iff_measure_inter_eq_mul
∀ {Ω : Type u_1} {_mΩ : MeasurableSpace Ω} {s t : Set Ω},
MeasurableSet s →
MeasurableSet t →
∀ (μ : autoParam (MeasureTheory.Measure Ω) ProbabilityTheory.indepSet_iff_measure_inter_eq_mul._auto_1)
[MeasureTheory.IsZeroOrProbabilityMeasure μ], ProbabilityTheory.IndepSet s t μ ↔ μ (s ∩ t) = μ s * μ t- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.IsZeroOrProbabilityMeasurestatement and proof · cited by 46
- ProbabilityTheory.IndepSetstatement · cited by 13
- ProbabilityTheory.indepSet_iff_indepSets_singletonproof · cited by 1
- ProbabilityTheory.indepSets_singleton_iffproof · cited by 1
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