Theorems · Theorem · probability
ProbabilityTheory.variance_dirac
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} [MeasurableSingletonClass Ω] (x : Ω),
ProbabilityTheory.variance X (MeasureTheory.Measure.dirac x) = 0- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSingletonClass
Around this declaration
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Cites11
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.integralproof · cited by 1,779
- sub_selfproof · cited by 996
- zero_powproof · cited by 361
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- ProbabilityTheory.variancestatement · cited by 104
- MeasureTheory.integral_diracproof · cited by 20
- ProbabilityTheory.variance_eq_integralproof · cited by 10
- MeasureTheory.aemeasurable_diracproof · cited by 3
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