Theorems · Theorem · probability
ProbabilityTheory.covarianceOperator_apply
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : MeasurableSpace E]
[inst_3 : BorelSpace E] {μ : MeasureTheory.Measure E} [inst_4 : CompleteSpace E],
MeasureTheory.MemLp id 2 μ → ∀ (x : E), (ProbabilityTheory.covarianceOperator μ) x = ∫ (y : E), inner ℝ x y • y ∂μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites28
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
- MeasureTheory.integralstatement and proof · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
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