Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.memLp_dual

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  (μ : MeasureTheory.Measure E) [ProbabilityTheory.IsGaussian μ] (L : StrongDual ℝ E) (p : ENNReal),
  p ≠ ⊤ → MeasureTheory.MemLp (⇑L) p μ

Defined in: Mathlib.Probability.Distributions.Gaussian.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace ProbabilityTheory.IsGaussian

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Cites28

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
TopologicalSpaceproof · cited by 24,529
RingHom.idstatement · cited by 18,349
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
MeasureTheory.integralproof · cited by 1,779
BorelSpacestatement and proof · cited by 1,602

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.IsGaussian.map_rotation_eq_self_of_forall_strongDual_eq_zeroproof · cited by 2
ProbabilityTheory.IsGaussian.integrable_dualproof · cited by 1