  We consider a version of height on polynomial spaces defined by the integral
over the normalized area measure on the unit disk. This natural analog of
Mahler's measure arises in connection with extremal problems for Bergman
spaces. It inherits many nice properties such as the multiplicative one.
However, this height is a lower bound for Mahler's measure, and it can be
substantially lower. We discuss some similarities and differences between the
two.
