Theorems · Theorem · probability

ProbabilityTheory.Kernel.density_mono_set

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} [inst : MeasurableSpace.CountablyGenerated γ] {κ : ProbabilityTheory.Kernel α (γ × β)}
  {ν : ProbabilityTheory.Kernel α γ},
  κ.fst ≤ ν → ∀ (a : α) (x : γ) {s s' : Set β}, s ⊆ s' → κ.density ν a x s ≤ κ.density ν a x s'

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

3 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGenerated