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Theorems · Theorem · probability

ProbabilityTheory.HasGaussianLaw.smul

∀ {Ω : Type u_1} {E : Type u_2} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} [inst : NormedAddCommGroup E]
  [inst_1 : MeasurableSpace E] [BorelSpace E] {X : Ω → E} [inst_3 : NormedSpace ℝ E] (c : ℝ),
  ProbabilityTheory.HasGaussianLaw X P → ProbabilityTheory.HasGaussianLaw (c • X) P
Defined in
Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
Cited by
2 results in Mathlib
Foundations
Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupMeasurableSpaceBorelSpaceNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.HasGaussianLaw.neg · cited by 1HasGaussianLaw.negProbabilityTheory.HasGaussianLaw.fun_smul · cited by 0HasGaussianLaw.fun_smulDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureBorelSpace · cited by 1602BorelSpaceProbabilityTheory.HasGaussianLaw · cited by 67ProbabilityTheory.HasGaus…ContinuousLinearMap.lsmul · cited by 66ContinuousLinearMap.lsmulProbabilityTheory.HasGaussianLaw.map · cited by 15HasGaussianLaw.mapHasGaussianLaw.smulCITED BYCITES

Cites10

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Cited by2

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