Theorems · Theorem · probability
ProbabilityTheory.covarianceBilinDual_of_not_memLp
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {mE : MeasurableSpace E} {μ : MeasureTheory.Measure E}
[inst_1 : NormedSpace ℝ E] [inst_2 : BorelSpace E],
¬MeasureTheory.MemLp id 2 μ → ∀ (L₁ L₂ : StrongDual ℝ E), ((ProbabilityTheory.covarianceBilinDual μ) L₁) L₂ = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- ENNRealstatement · cited by 9,879
- ContinuousLinearMapstatement · cited by 5,352
- MeasureTheory.integralproof · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- StrongDualstatement and proof · cited by 459
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceBilin_of_not_memLpproof · cited by 2
- ProbabilityTheory.covarianceBilinDual_self_nonnegproof · cited by 1