Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndep.iIndepSets

∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {_mα : MeasurableSpace α} {_mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {m : ι → MeasurableSpace Ω} {s : ι → Set (Set Ω)},
  (∀ (n : ι), m n = MeasurableSpace.generateFrom (s n)) →
    ProbabilityTheory.Kernel.iIndep m κ μ → ProbabilityTheory.Kernel.iIndepSets s 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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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
Finsetproof · cited by 13,712
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.iIndepstatement and proof · cited by 33
ProbabilityTheory.Kernel.iIndepSetsstatement · cited by 21

Cited by5

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.iIndepSet.indep_generateFrom_of_disjointproof · cited by 4
ProbabilityTheory.Kernel.iIndepSet_iff_iIndepSets_singletonproof · cited by 3
ProbabilityTheory.Kernel.iIndepSet.meas_biInterproof · cited by 1
ProbabilityTheory.iCondIndep.iCondIndepSetsproof · cited by 0
ProbabilityTheory.iIndep.iIndepSetsproof · cited by 0