Theorems · Theorem · probability

ProbabilityTheory.stdGaussian_map

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  [inst_3 : MeasurableSpace E] [BorelSpace E] {F : Type u_3} [inst_5 : NormedAddCommGroup F]
  [inst_6 : InnerProductSpace ℝ F] [inst_7 : MeasurableSpace F] [BorelSpace F] (f : E ≃ₗᵢ[ℝ] F),
  MeasureTheory.Measure.map (⇑f) (ProbabilityTheory.stdGaussian E) = ProbabilityTheory.stdGaussian F

Defined in: Mathlib.Probability.Distributions.Gaussian.Multivariate
Cited by: 1 results in Mathlib
Foundations: Depth 318 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace NormedAddCommGroup InnerProductSpace MeasurableSpace BorelSpace

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Cites32

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
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpaceproof · cited by 12,499
MeasureTheory.Measurestatement · cited by 10,939
RingHomproof · cited by 10,189
NontriviallyNormedFieldproof · cited by 8,742
Norm.normproof · cited by 5,413
InnerProductSpacestatement and proof · cited by 3,523
FiniteDimensionalstatement and proof · cited by 1,854

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasisproof · cited by 0