Theorems · Theorem · probability
ProbabilityTheory.variance_nonneg
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} (X : Ω → ℝ) (μ : MeasureTheory.Measure Ω), 0 ≤ ProbabilityTheory.variance X μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 252 from the axioms · 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
- ProbabilityTheory.variancestatement · cited by 104
- ENNReal.toReal_nonnegproof · cited by 86
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussian.charFunDual_eqproof · cited by 9
- ProbabilityTheory.isGaussian_iff_charFunDual_eqproof · cited by 2
- ProbabilityTheory.IsGaussian.nullSingletonClassproof · cited by 1
- ProbabilityTheory.strong_law_aux1proof · cited by 1