Theorems · Theorem · probability

ProbabilityTheory.iIndepFun.map_fun_eq_pi_map

∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : Fintype ι]
  {β : ι → Type u_11} {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  (∀ (i : ι), AEMeasurable (f i) μ) →
    ProbabilityTheory.iIndepFun f μ →
      MeasureTheory.Measure.map (fun ω i => f i ω) μ =
        MeasureTheory.Measure.pi fun i => MeasureTheory.Measure.map (f i) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype

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Cites30

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Finsetproof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Fintypestatement and proof · cited by 7,736
Set.preimageproof · cited by 4,946
Set.univproof · cited by 3,945
Finset.univproof · cited by 3,473
MeasurableSetproof · cited by 3,075
Finset.prodproof · cited by 2,356

Cited by4

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepFun_iff_map_fun_eq_pi_mapproof · cited by 6
ProbabilityTheory.iIndepFun.map_fun_eq_infinitePi_map₀proof · cited by 3
ProbabilityTheory.iIndepFun.integral_fun_prod_compproof · cited by 2
ProbabilityTheory.iIndepFun.hasLaw_piproof · cited by 1