Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.integral_dual

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  {μ : MeasureTheory.Measure E} [ProbabilityTheory.IsGaussian μ] [CompleteSpace E] [SecondCountableTopology E]
  (L : StrongDual ℝ E), ∫ (x : E), L x ∂μ = L (∫ (x : E), x ∂μ)

Defined in

Mathlib.Probability.Distributions.Gaussian.Fernique

Cited by

3 results in Mathlib

Foundations

Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceProbabilityTheory.IsGaussianCompleteSpaceSecondCountableTopology