Theorems · Definition · probability

ProbabilityTheory.Kernel.comap

{α : Type u_1} →
  {β : Type u_2} →
    {mα : MeasurableSpace α} →
      {mβ : MeasurableSpace β} →
        {γ : Type u_4} →
          {mγ : MeasurableSpace γ} →
            ProbabilityTheory.Kernel α β → (g : γ → α) → Measurable g → ProbabilityTheory.Kernel γ β

Pullback of a kernel, such that for each set s comap κ g hg c s = κ (g c) s. We include measurability in the assumptions instead of using junk values to make sure that typeclass inference can infer that the comap of a Markov kernel is again a Markov kernel.

Defined in

Mathlib.Probability.Kernel.Composition.MapComap

Cited by

34 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound