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Theorems · Theorem · probability

ProbabilityTheory.condIndepSet_iff_condIndepSets_singleton

∀ {Ω : Type u_1} (m' : MeasurableSpace Ω) {mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] (hm' : m' ≤ mΩ)
  {s t : Set Ω},
  MeasurableSet s →
    MeasurableSet t →
      ∀ (μ : MeasureTheory.Measure Ω) [inst_1 : MeasureTheory.IsFiniteMeasure μ],
        ProbabilityTheory.CondIndepSet m' hm' s t μ ↔ ProbabilityTheory.CondIndepSets m' hm' {s} {t} μ
Defined in
Mathlib.Probability.Independence.Conditional
Cited by
1 results in Mathlib
Foundations
Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
StandardBorelSpaceMeasureTheory.IsFiniteMeasure
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Around this declaration

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ProbabilityTheory.condIndepSet_iff · cited by 0ProbabilityTheory.condInd…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurableSet · cited by 3075MeasurableSetMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…StandardBorelSpace · cited by 304StandardBorelSpaceMeasureTheory.Measure.trim · cited by 286Measure.trimProbabilityTheory.condExpKernel · cited by 49ProbabilityTheory.condExp…ProbabilityTheory.CondIndepSets · cited by 21ProbabilityTheory.CondInd…ProbabilityTheory.CondIndepSet · cited by 11ProbabilityTheory.CondInd…ProbabilityTheory.Kernel.indepSet_iff_indepSets_singleton · cited by 3Kernel.indepSet_iff_indep…ProbabilityTheory.condIndepSe…CITED BYCITES

Cites11

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Cited by1

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