Assume that $B_2\subset \mathbb{C}^2$ is an unit ball and let $d\tau(z) = dV(z)/(1-|z|^2)^3$ be associated Bergman measure on $B_2$. Then for $\Omega\subset B_2$ we define the $\tau$-volume of $\Omega$ by $$\tau(\Omega)=\int_{\Omega}d\tau(z),$$ provided the last quantity is finite. What is the natural way to define the measure of the hypersurface $\partial \Omega$, provided it is smooth?
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