Theorems · Theorem · probability
ProbabilityTheory.condIndep_iff_condIndepSets
∀ {Ω : Type u_1} (m' m₁ m₂ : MeasurableSpace Ω) {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 ↔
ProbabilityTheory.CondIndepSets m' hm' {s | MeasurableSet s} {s | MeasurableSet s} μ- Cited by
- 1 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.
Cites12
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
- Set.ofPredstatement and proof · cited by 6,101
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- StandardBorelSpacestatement and proof · cited by 304
- MeasureTheory.Measure.trimproof · cited by 286
- ProbabilityTheory.condExpKernelproof · cited by 49
- ProbabilityTheory.CondIndepstatement · cited by 30
- ProbabilityTheory.Kernel.IndepSetsproof · cited by 27
- ProbabilityTheory.CondIndepSetsstatement · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condIndep_iffproof · cited by 1