Theorems · Theorem · probability

MeasureTheory.pdf.uniformPDF_eq_pdf

∀ {E : Type u_1} [inst : MeasurableSpace E] {μ : MeasureTheory.Measure E} {Ω : Type u_2} {x : MeasurableSpace Ω}
  {ℙ : MeasureTheory.Measure Ω} {X : Ω → E} {s : Set E},
  MeasurableSet s →
    MeasureTheory.pdf.IsUniform X s ℙ μ → (fun x => MeasureTheory.pdf.uniformPDF s x μ) =ᵐ[μ] MeasureTheory.pdf X ℙ μ

Check that indeed any uniform random variable has the uniformPDF.

Defined in

Mathlib.Probability.Distributions.Uniform

Cited by

0 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace