Theorems · Theorem · probability

ProbabilityTheory.iIndepFun.hasGaussianLaw_sum

∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E] [SecondCountableTopology E] [CompleteSpace E]
  {ι : Type u_3} [inst_6 : Fintype ι] {X : ι → Ω → E},
  (∀ (i : ι), ProbabilityTheory.HasGaussianLaw (X i) P) →
    ProbabilityTheory.iIndepFun X P → ProbabilityTheory.HasGaussianLaw (∑ i, X i) P

Defined in: Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence
Cited by: 0 results in Mathlib
Foundations: Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace SecondCountableTopology CompleteSpace Fintype

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Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
Fintypestatement and proof · cited by 7,736
Finset.sumstatement · cited by 5,195
Finset.univstatement · cited by 3,473
CompleteSpacestatement and proof · cited by 2,532
BorelSpacestatement and proof · cited by 1,602
SecondCountableTopologystatement and proof · cited by 750
ProbabilityTheory.iIndepFunstatement and proof · cited by 138

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