Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.nullSingletonClass

∀ {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],
  (∀ (x : E), μ ≠ MeasureTheory.Measure.dirac x) → MeasureTheory.NullSingletonClass μ

If a Gaussian measure is not a Dirac, then it has value zero on singletons.

Defined in

Mathlib.Probability.Distributions.Gaussian.Fernique

Cited by

1 results in Mathlib

Foundations

Depth 313 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceProbabilityTheory.IsGaussianCompleteSpaceSecondCountableTopology