Theorems · Theorem · probability
ProbabilityTheory.covarianceBilinDual_self_nonneg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E}
[inst_1 : NormedSpace ℝ E] [inst_2 : BorelSpace E] (L : StrongDual ℝ E),
0 ≤ ((ProbabilityTheory.covarianceBilinDual μ) L) L- 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 · 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
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ContinuousLinearMapstatement · cited by 5,352
- BorelSpacestatement and proof · cited by 1,602
- StrongDualstatement and proof · cited by 459
- MeasureTheory.MemLpproof · cited by 457
- ProbabilityTheory.covarianceBilinDualstatement · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isPosSemidef_covarianceBilinDualproof · cited by 4