Theorems · Theorem · probability

ProbabilityTheory.compProd_posterior_eq_swap_comp

∀ {Ω : Type u_1} {𝓧 : Type u_2} {mΩ : MeasurableSpace Ω} {m𝓧 : MeasurableSpace 𝓧} {κ : ProbabilityTheory.Kernel Ω 𝓧}
  {μ : MeasureTheory.Measure Ω} [inst : MeasureTheory.IsFiniteMeasure μ] [inst_1 : ProbabilityTheory.IsFiniteKernel κ]
  [inst_2 : StandardBorelSpace Ω] [inst_3 : Nonempty Ω],
  (μ.bind ⇑κ).compProd (ProbabilityTheory.posterior κ μ) = (μ.compProd κ).bind ⇑(ProbabilityTheory.Kernel.swap Ω 𝓧)

Defined in

Mathlib.Probability.Kernel.Posterior

Cited by

4 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasureProbabilityTheory.IsFiniteKernelStandardBorelSpaceNonempty