Theorems · Theorem · probability
ProbabilityTheory.condIndepSet_iff_condIndep
∀ {Ω : Type u_1} (m' : MeasurableSpace Ω) {mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] (hm' : m' ≤ mΩ)
(s t : Set Ω) (μ : MeasureTheory.Measure Ω) [inst_1 : MeasureTheory.IsFiniteMeasure μ],
ProbabilityTheory.CondIndepSet m' hm' s t μ ↔
ProbabilityTheory.CondIndep m' (MeasurableSpace.generateFrom {s}) (MeasurableSpace.generateFrom {t}) hm' μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- StandardBorelSpacestatement and proof · cited by 304
- MeasureTheory.Measure.trimproof · cited by 286
- MeasurableSpace.generateFromstatement and proof · cited by 172
- ProbabilityTheory.condExpKernelproof · cited by 49
- ProbabilityTheory.Kernel.Indepproof · cited by 42
- ProbabilityTheory.CondIndepstatement · cited by 30
- ProbabilityTheory.CondIndepSetstatement · cited by 11
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