Conditional product law of the recursive augmented kernel

The recursively measurable kernel used for the finite mixture construction has, at every fixed latent parameter vector, exactly the ordinary finite product of the selected one-coordinate laws.

theorem Feige.recursiveAugmentedKernel_apply_eq_conditionalProduct (n : ℕ) (p : Fin n → AugmentedTwoPointParams) : (recursiveAugmentedKernel n) p = augmentedConditionalProduct p