Theorems · Theorem · probability
ProbabilityTheory.gaussianReal_map_linearMap
∀ {μ : ℝ} {v : NNReal} (L : ℝ →ₗ[ℝ] ℝ),
MeasureTheory.Measure.map (⇑L) (ProbabilityTheory.gaussianReal μ v) =
ProbabilityTheory.gaussianReal (L μ) ((L 1 ^ 2).toNNReal * v)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 294 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 and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- MeasureTheory.Measurestatement and proof · cited by 10,939
- LinearMapstatement and proof · cited by 10,215
- NNRealstatement and proof · cited by 4,310
- mul_oneproof · cited by 3,885
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- Real.toNNRealstatement and proof · cited by 267
- sq_nonnegproof · cited by 106
- even_two_mulproof · cited by 102
- Even.pow_nonnegproof · cited by 94
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_linearMap_gaussianRealproof · cited by 1
- ProbabilityTheory.integral_linearMap_gaussianRealproof · cited by 1
- ProbabilityTheory.gaussianReal_map_continuousLinearMapproof · cited by 0