Theorems · Theorem · probability

ProbabilityTheory.iIndepFun.indepFun

∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {β : ι → Type u_6}
  {m : (x : ι) → MeasurableSpace (β x)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.iIndepFun f μ → ∀ {i j : ι}, i ≠ j → ProbabilityTheory.IndepFun (f i) (f j) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ProbabilityTheory.IndepFunstatement · cited by 192
ProbabilityTheory.iIndepFunstatement and proof · cited by 138
ProbabilityTheory.Kernel.iIndepFun.indepFunproof · cited by 2

Cited by3

Results whose statement or proof uses this declaration.

ProbabilityTheory.HasIndepIncrements.indepFun_sub_subproof · cited by 1
ProbabilityTheory.variance_sum_piproof · cited by 1
MeasureTheory.Measure.infinitePi_map_eval_prodproof · cited by 0