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67aee1d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | 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
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