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Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.integrable_fun_id

∀ {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] [CompleteSpace E] [SecondCountableTopology E],
  MeasureTheory.Integrable (fun x => x) μ

Eta-expanded form of ProbabilityTheory.IsGaussian.integrable_id

Defined in
Mathlib.Probability.Distributions.Gaussian.Fernique
Cited by
1 results in Mathlib
Foundations
Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceProbabilityTheory.IsGaussianCompleteSpaceSecondCountableTopology
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Around this declaration

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

ProbabilityTheory.integral_id_multivariateGaussian · cited by 5ProbabilityTheory.integra…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureCompleteSpace · cited by 2532CompleteSpaceBorelSpace · cited by 1602BorelSpaceMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableSecondCountableTopology · cited by 750SecondCountableTopologyProbabilityTheory.IsGaussian · cited by 48ProbabilityTheory.IsGauss…ProbabilityTheory.IsGaussian.integrable_id · cited by 11IsGaussian.integrable_idIsGaussian.integrable_fun_idCITED BYCITES

Cites11

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Cited by1

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