Theorems · Theorem · probability
ProbabilityTheory.IndepSet_iff
∀ {Ω : Type u_1} {x : MeasurableSpace Ω} (s t : Set Ω) (μ : MeasureTheory.Measure Ω),
ProbabilityTheory.IndepSet s t μ ↔ ∀ (t1 t2 : Set Ω), MeasurableSet t1 → MeasurableSet t2 → μ (t1 ∩ t2) = μ t1 * μ t2- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- MeasurableSpace.generateFromstatement and proof · cited by 172
- ProbabilityTheory.IndepSetstatement · cited by 13
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