Theorems · Theorem · probability

ProbabilityTheory.Kernel.meas_countablePartitionSet_le_of_fst_le

∀ {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 →
    ∀ (n : ℕ) (a : α) (x : γ) (s : Set β),
      (κ a) (MeasurableSpace.countablePartitionSet n x ×ˢ s) ≤ (ν a) (MeasurableSpace.countablePartitionSet n x)

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

4 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGenerated