φ m , we have the same distribution: Note that the last transformation is because φ m ⊂ φ m−1 ; had it not been the case,p m would depend on the combination of φ m and φ m−1 and require multiple parameters to be represented on its entire domain w n 1 ∈ φ m .
after n iterations, we have: we have constructedp n (w i |φ n ) using the same recursive representation as in Eq.