Theorems · Theorem · probability

ProbabilityTheory.indep_iSup_of_disjoint

∀ {Ω : Type u_1} {ι : Type u_2} {m : ι → MeasurableSpace Ω} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω},
  (∀ (i : ι), m i ≤ _mΩ) →
    ProbabilityTheory.iIndep m μ →
      ∀ {S T : Set ι}, Disjoint S T → ProbabilityTheory.Indep (⨆ i ∈ S, m i) (⨆ i ∈ T, m i) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

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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
iSupstatement · cited by 2,415
Disjointstatement and proof · cited by 2,201
ProbabilityTheory.Indepstatement · cited by 43
ProbabilityTheory.iIndepstatement and proof · cited by 30
ProbabilityTheory.Kernel.indep_iSup_of_disjointproof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepFun.indep_comap_natural_of_ltproof · cited by 1