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Theorems · Definition · probability

ProbabilityTheory.gaussianReal

ℝ → NNReal → MeasureTheory.Measure ℝ

A Gaussian distribution on with mean μ and variance v.

Defined in
Mathlib.Probability.Distributions.Gaussian.Real
Cited by
77 results in Mathlib
Foundations
Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

ProbabilityTheory.stdGaussian · cited by 14ProbabilityTheory.stdGaus…ProbabilityTheory.IsGaussian.charFunDual_eq · cited by 9IsGaussian.charFunDual_eqProbabilityTheory.charFun_gaussianReal · cited by 7ProbabilityTheory.charFun…ProbabilityTheory.gaussianReal_of_var_ne_zero · cited by 7ProbabilityTheory.gaussia…ProbabilityTheory.gaussianReal_zero_var · cited by 7ProbabilityTheory.gaussia…ProbabilityTheory.integral_id_gaussianReal · cited by 6ProbabilityTheory.integra…ProbabilityTheory.IsGaussian.map_eq_gaussianReal · cited by 6IsGaussian.map_eq_gaussia…ProbabilityTheory.variance_id_gaussianReal · cited by 4ProbabilityTheory.varianc…ProbabilityTheory.gaussianReal_map_const_mul · cited by 4ProbabilityTheory.gaussia…ProbabilityTheory.isGaussian_iff_gaussian_charFunDual · cited by 4ProbabilityTheory.isGauss…ProbabilityTheory.mgf_fun_id_gaussianReal · cited by 3ProbabilityTheory.mgf_fun…ProbabilityTheory.mgf_gaussianReal · cited by 3ProbabilityTheory.mgf_gau…ProbabilityTheory.complexMGF_id_gaussianReal · cited by 3ProbabilityTheory.complex…ProbabilityTheory.IsPreBrownianReal.hasLaw_eval · cited by 3IsPreBrownianReal.hasLaw_…ProbabilityTheory.gaussianReal_map_add_const · cited by 3ProbabilityTheory.gaussia…Real · cited by 25697RealMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureNNReal · cited by 4310NNRealMeasureTheory.MeasureSpace.volume · cited by 1323MeasureSpace.volumeMeasureTheory.Measure.withDensity · cited by 265Measure.withDensityMeasureTheory.Measure.dirac · cited by 210Measure.diracProbabilityTheory.gaussianPDF · cited by 18ProbabilityTheory.gaussia…ProbabilityTheory.gaussianRealCITED BYCITES

Cites7

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Cited by80

Results whose statement or proof uses this declaration.