Theorems · Theorem · probability

ProbabilityTheory.integral_gaussianReal_eq_integral_smul

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {μ : ℝ} {v : NNReal} {f : ℝ → E},
  v ≠ 0 → ∫ (x : ℝ), f x ∂ProbabilityTheory.gaussianReal μ v = ∫ (x : ℝ), ProbabilityTheory.gaussianPDFReal μ v x • f x

Defined in

Mathlib.Probability.Distributions.Gaussian.Real

Cited by

1 results in Mathlib

Foundations

Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace