Theorems · Theorem · probability
ProbabilityTheory.covarianceBilin_self
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : MeasurableSpace E]
[inst_3 : BorelSpace E] {μ : MeasureTheory.Measure E} [CompleteSpace E] [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp id 2 μ →
∀ (x : E), ((ProbabilityTheory.covarianceBilin μ) x) x = ProbabilityTheory.variance (fun u => inner ℝ x u) μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- BorelSpacestatement and proof · cited by 1,602
- Inner.innerstatement and proof · cited by 1,089
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussian.charFun_eq'proof · cited by 2