Theorems · Theorem · probability

ProbabilityTheory.BrownianReal.variance_projectiveFamily

∀ (I : Finset NNReal) (f : (↥I → ℝ) → ℝ),
  ProbabilityTheory.variance f (ProbabilityTheory.BrownianReal.projectiveFamily I) =
    ProbabilityTheory.variance (f ∘ WithLp.ofLp)
      (ProbabilityTheory.multivariateGaussian 0 (ProbabilityTheory.BrownianReal.covMatrix I))

Defined in: Mathlib.Probability.BrownianMotion.GaussianProjectiveFamily
Cited by: 1 results in Mathlib
Foundations: Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites16

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

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
Finsetstatement and proof · cited by 13,712
MeasureTheory.Measureproof · cited by 10,939
ENNRealstatement · cited by 9,879
NNRealstatement and proof · cited by 4,310
WithLpstatement · cited by 345
WithLp.ofLpstatement and proof · cited by 323
EuclideanSpacestatement · cited by 307
MeasurableEquiv.symmproof · cited by 155
ProbabilityTheory.variancestatement and proof · cited by 104
MeasurableEquiv.toLpproof · cited by 27

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.BrownianReal.variance_fun_projectiveFamilyproof · cited by 0