Theorems · Definition · probability
ProbabilityTheory.evariance
{Ω : Type u_1} → {mΩ : MeasurableSpace Ω} → (Ω → ℝ) → MeasureTheory.Measure Ω → ENNRealThe ℝ≥0∞-valued variance of a real-valued random variable defined as the Lebesgue integral of
‖X - 𝔼[X]‖^2.
- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ENNRealstatement · cited by 9,879
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.lintegralproof · cited by 1,152
- ENorm.enormproof · cited by 715
Cited by23
Results whose statement or proof uses this declaration.
- ProbabilityTheory.varianceproof · cited by 104
- ProbabilityTheory.variance_const_mulproof · cited by 5
- ProbabilityTheory.evariance_lt_topstatement · cited by 3
- ProbabilityTheory.IdentDistrib.variance_eqproof · cited by 2
- ProbabilityTheory.evariance_eq_topstatement and proof · cited by 2
- ProbabilityTheory.evariance_ne_topstatement · cited by 2
- ProbabilityTheory.variance_congrproof · cited by 2
- ProbabilityTheory.ofReal_variancestatement and proof · cited by 2
- ProbabilityTheory.meas_ge_le_variance_div_sqproof · cited by 1
- MeasureTheory.MemLp.ofReal_variance_eqstatement · cited by 1
- ProbabilityTheory.evariance_congrstatement · cited by 1
- ProbabilityTheory.evariance_eq_lintegral_ofRealstatement · cited by 1