| import Mathlib | |
| import OAI.Analysis.HardSphere.Kernels.FiniteKernelPi | |
| namespace OAI | |
| section | |
| section | |
| noncomputable section | |
| open MeasureTheory ProbabilityTheory Set | |
| open scoped ENNReal | |
| namespace HardSphere.Comparison | |
| variable {W I : Type*} [MeasurableSpace W] [Fintype I] | |
| {X : I→Type*} [∀i,MeasurableSpace (X i)] | |
| lemma finiteKernelPi_finite (κ : ∀i,Kernel W (X i)) [∀i,IsFiniteKernel (κ i)] : | |
| IsFiniteKernel (finiteKernelPi κ) := inferInstance | |
| instance finiteKernelPi_markov (κ : ∀i,Kernel W (X i)) [∀i,IsMarkovKernel (κ i)] : | |
| IsMarkovKernel (finiteKernelPi κ) := by | |
| constructor | |
| intro w | |
| rw [finiteKernelPi_apply] | |
| infer_instance | |
| end HardSphere.Comparison | |
| end | |
| end | |
| end | |
| end OAI | |