Theorems · Theorem · probability
ProbabilityTheory.IsGaussian.memLp_id
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
[CompleteSpace E] [SecondCountableTopology E] (μ : MeasureTheory.Measure E) [ProbabilityTheory.IsGaussian μ]
(p : ENNReal), p ≠ ⊤ → MeasureTheory.MemLp id p μA Gaussian measure has moments of all orders.
That is, the identity is in L^p for all finite p.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
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
- TopologicalSpaceproof · cited by 24,529
- 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
- Norm.normproof · cited by 5,413
- NNRealproof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- LT.lt.leproof · cited by 2,189
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussian.integrable_idproof · cited by 11
- ProbabilityTheory.IsGaussian.memLp_two_idproof · cited by 10
- ProbabilityTheory.IsGaussian.integral_dualproof · cited by 3
- ProbabilityTheory.HasGaussianLaw.memLpproof · cited by 2