Berger measure for

In this note, we get the Berger measure of the weighted shift S ( a , b , c , d ) with weights α n : = a n + b c n + d ( a , b , c , d > 0 and n ⩾ 0 ) as well as its p-subshift. Then we will give examples from analytic function theory to illustrate that the necessary condition given by Curto and Yoon (2006) [12] for subnormality of 2-variable weighted shift is not sufficient. Furthermore, we will do some calculations about subnormal backward extension of S ( a , b , c , d ) .