Theorems · Theorem · probability
ProbabilityTheory.variance_congr
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X Y : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
X =ᵐ[μ] Y → ProbabilityTheory.variance X μ = ProbabilityTheory.variance Y μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- ENNReal.toRealproof · cited by 859
- ProbabilityTheory.variancestatement · cited by 104
- ProbabilityTheory.evarianceproof · cited by 22
- ProbabilityTheory.evariance_congrproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun.variance_addproof · cited by 2
- ProbabilityTheory.IndepFun.variance_sumproof · cited by 2