Theorems · Definition · probability
ProbabilityTheory.variance
{Ω : Type u_1} → {mΩ : MeasurableSpace Ω} → (Ω → ℝ) → MeasureTheory.Measure Ω → ℝThe ℝ-valued variance of a real-valued random variable defined by applying ENNReal.toReal
to evariance.
- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 251 from the axioms, rests on 6,486 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNReal.toRealproof · cited by 859
- ProbabilityTheory.evarianceproof · cited by 22
Cited by106
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_mapstatement and proof · cited by 11
- ProbabilityTheory.covariance_selfstatement and proof · cited by 11
- ProbabilityTheory.variance_eq_integralstatement · cited by 10
- ProbabilityTheory.IsGaussian.charFunDual_eqstatement and proof · cited by 9
- ProbabilityTheory.IsGaussian.map_eq_gaussianRealstatement · cited by 6
- ProbabilityTheory.variance_addstatement and proof · cited by 5
- ProbabilityTheory.variance_const_mulstatement and proof · cited by 5
- ProbabilityTheory.covarianceBilinDual_self_eq_variancestatement and proof · cited by 5
- ProbabilityTheory.variance_eq_substatement · cited by 4
- ProbabilityTheory.variance_id_gaussianRealstatement · cited by 4
- ProbabilityTheory.variance_nonnegstatement · cited by 4
- ProbabilityTheory.HasGaussianLaw.charFunDual_map_eqstatement and proof · cited by 4