Theorems · Theorem · probability
ProbabilityTheory.indepSets_singleton_iff
∀ {Ω : Type u_1} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {s t : Set Ω},
ProbabilityTheory.IndepSets {s} {t} μ ↔ μ (s ∩ t) = μ s * μ t- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 1 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.
- 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
- Filter.Eventuallyproof · cited by 3,134
- MeasureTheory.ae_dirac_eqproof · cited by 31
- ProbabilityTheory.IndepSetsstatement · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.indepSet_iff_measure_inter_eq_mulproof · cited by 0