Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.map_eq_gaussianReal

∀ {E : Type u_1} {inst : TopologicalSpace E} {inst_1 : AddCommMonoid E} {inst_2 : Module ℝ E} {mE : MeasurableSpace E}
  {μ : MeasureTheory.Measure E} [self : ProbabilityTheory.IsGaussian μ] (L : StrongDual ℝ E),
  MeasureTheory.Measure.map (⇑L) μ =
    ProbabilityTheory.gaussianReal (∫ (x : E), L x ∂μ) (ProbabilityTheory.variance (⇑L) μ).toNNReal

Defined in

Mathlib.Probability.Distributions.Gaussian.Basic

Cited by

6 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsGaussian