Theorems · Theorem · probability

MeasureTheory.pdf.IsUniform.pdf_eq_zero_of_measure_eq_zero_or_top

∀ {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},
  MeasureTheory.pdf.IsUniform X s ℙ μ → μ s = 0 ∨ μ s = ⊤ → MeasureTheory.pdf X ℙ μ =ᵐ[μ] 0

Defined in

Mathlib.Probability.Distributions.Uniform

Cited by

2 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace