Theorems · Theorem · probability
ProbabilityTheory.covarianceBilin_comm
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : MeasurableSpace E]
[inst_3 : BorelSpace E] {μ : MeasureTheory.Measure E} (x y : E),
((ProbabilityTheory.covarianceBilin μ) x) y = ((ProbabilityTheory.covarianceBilin μ) y) x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- BorelSpacestatement and proof · cited by 1,602
- InnerProductSpace.toDualMapproof · cited by 26
- ProbabilityTheory.covarianceBilinstatement and proof · cited by 25
- ProbabilityTheory.covarianceBilinDualproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isPosSemidef_covarianceBilinproof · cited by 1