Theorems · Theorem · probability

ProbabilityTheory.Kernel.Indep.indepSets

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {_mΩ : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω}
  {μ : MeasureTheory.Measure α} {s1 s2 : Set (Set Ω)},
  ProbabilityTheory.Kernel.Indep (MeasurableSpace.generateFrom s1) (MeasurableSpace.generateFrom s2) κ μ →
    ProbabilityTheory.Kernel.IndepSets s1 s2 κ μ

Defined in: Mathlib.Probability.Independence.Kernel.Indep
Cited by: 5 results in Mathlib
Foundations: Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites8

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
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasurableSpace.generateFromstatement and proof · cited by 172
MeasurableSpace.measurableSet_generateFromproof · cited by 46
ProbabilityTheory.Kernel.Indepstatement and proof · cited by 42
ProbabilityTheory.Kernel.IndepSetsstatement · cited by 27

Cited by5

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.indep_iSup_of_directed_leproof · cited by 5
ProbabilityTheory.Kernel.indepSet_iff_indepSets_singletonproof · cited by 3
ProbabilityTheory.Kernel.IndepSet.measure_inter_eq_mulproof · cited by 1
ProbabilityTheory.CondIndep.condIndepSetsproof · cited by 0
ProbabilityTheory.Indep.indepSetsproof · cited by 0