Theorems · Theorem · probability
ProbabilityTheory.variance_linearMap_gaussianReal
∀ {μ : ℝ} {v : NNReal} (L : ℝ →ₗ[ℝ] ℝ),
ProbabilityTheory.variance (⇑L) (ProbabilityTheory.gaussianReal μ v) = ↑(L 1 ^ 2).toNNReal * ↑v- Cited by
- 1 results in Mathlib
- Foundations
- Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 18,349
- MeasureTheory.Measureproof · cited by 10,939
- LinearMapstatement and proof · cited by 10,215
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- Real.toNNRealstatement and proof · cited by 267
- ProbabilityTheory.variancestatement and proof · cited by 104
- ProbabilityTheory.gaussianRealstatement · cited by 77
- Continuous.aemeasurableproof · cited by 21
- IsModuleTopology.continuous_of_linearMapproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_continuousLinearMap_gaussianRealproof · cited by 0