Theorems · Theorem · probability
ProbabilityTheory.CondIndep.condIndepSet_of_measurableSet
∀ {Ω : Type u_1} {m' m₁ m₂ mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
{μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ],
ProbabilityTheory.CondIndep m' m₁ m₂ hm' μ →
∀ {s t : Set Ω}, MeasurableSet s → MeasurableSet t → ProbabilityTheory.CondIndepSet m' hm' s t μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.IsFiniteMeasurestatement and proof · cited by 1,078
- StandardBorelSpacestatement and proof · cited by 304
- ProbabilityTheory.CondIndepstatement and proof · cited by 30
- ProbabilityTheory.CondIndepSetstatement · cited by 11
- ProbabilityTheory.Kernel.Indep.indepSet_of_measurableSetproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBotproof · cited by 0
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTopproof · cited by 0