Theorems · Theorem · probability
ProbabilityTheory.variance_sub_const
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω}
[MeasureTheory.IsProbabilityMeasure μ],
MeasureTheory.AEStronglyMeasurable X μ →
∀ (c : ℝ), ProbabilityTheory.variance (fun ω => X ω - c) μ = ProbabilityTheory.variance X μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- sub_eq_add_negproof · cited by 1,023
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- ProbabilityTheory.variancestatement and proof · cited by 104
- ProbabilityTheory.variance_add_constproof · cited by 2
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