Mathlib Map

Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.eq_gaussianReal

∀ (μ : MeasureTheory.Measure ℝ),
  ProbabilityTheory.IsGaussian μ →
    μ = ProbabilityTheory.gaussianReal (∫ (x : ℝ), id x ∂μ) (ProbabilityTheory.variance id μ).toNNReal

A Gaussian measure over ℝ is some gaussianReal.

Defined in
Mathlib.Probability.Distributions.Gaussian.Basic
Cited by
2 results in Mathlib
Foundations
Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ProbabilityTheory.HasGaussianLaw.map_eq_gaussianReal · cited by 2HasGaussianLaw.map_eq_gau…ProbabilityTheory.isGaussian_of_isGaussian_map · cited by 1ProbabilityTheory.isGauss…Real · cited by 25697RealMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.integral · cited by 1779MeasureTheory.integralReal.toNNReal · cited by 267Real.toNNRealContinuousLinearMap.id · cited by 233ContinuousLinearMap.idProbabilityTheory.variance · cited by 104ProbabilityTheory.varianceProbabilityTheory.gaussianReal · cited by 77ProbabilityTheory.gaussia…ProbabilityTheory.IsGaussian · cited by 48ProbabilityTheory.IsGauss…MeasureTheory.Measure.map_id · cited by 29Measure.map_idProbabilityTheory.IsGaussian.map_eq_gaussianReal · cited by 6IsGaussian.map_eq_gaussia…IsGaussian.eq_gaussianRealCITED BYCITES

Cites10

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

Cited by2

Results whose statement or proof uses this declaration.