Theorems · Theorem · probability

ProbabilityTheory.HasGaussianLaw.memLp

∀ {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] [CompleteSpace E]
  [SecondCountableTopology E], ProbabilityTheory.HasGaussianLaw X P → ∀ {p : ENNReal}, p ≠ ⊤ → MeasureTheory.MemLp X p P

A Gaussian random variable has moments of all orders.

Defined in: Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup MeasurableSpace BorelSpace NormedSpace CompleteSpace SecondCountableTopology

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

Cites17

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

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
ENNRealstatement and proof · cited by 9,879
Top.topstatement and proof · cited by 9,680
CompleteSpacestatement and proof · cited by 2,532
BorelSpacestatement and proof · cited by 1,602
MeasureTheory.Measure.mapproof · cited by 858
SecondCountableTopologystatement and proof · cited by 750
MeasureTheory.MemLpstatement and proof · cited by 457

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.HasGaussianLaw.memLp_twoproof · cited by 13
ProbabilityTheory.HasGaussianLaw.integrableproof · cited by 7