Theorems · Theorem · probability

ProbabilityTheory.iIndepFun.precomp

∀ {Ω : Type u_1} {ι : Type u_2} {x : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ι' : Type u_6} {g : ι' → ι}
  {β : ι → Type u_7} {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  Function.Injective g → ProbabilityTheory.iIndepFun f μ → ProbabilityTheory.iIndepFun (fun i => f (g i)) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites4

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.iIndepFunstatement and proof · cited by 138
ProbabilityTheory.Kernel.iIndepFun.precompproof · cited by 2

Cited by6

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepFun_iff_finsetproof · cited by 4
ProbabilityTheory.iIndepFun.charFunDual_map_finsetSum_eq_prodproof · cited by 4
ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFunproof · cited by 2
ProbabilityTheory.HasIndepIncrements.natproof · cited by 2
ProbabilityTheory.HasIndepIncrements.of_natproof · cited by 1
MeasureTheory.Measure.map_infinitePi_infinitePi_of_injproof · cited by 0