  In convex geometry, the Blaschke surface area measure on the boundary of a
convex domain can be interpreted in terms of the complexity of approximating
polyhedra. In response to a question raised by D. Barrett, this approach is
formulated in the holomorphic setting to establish an alternate interpretation
of Fefferman's hypersurface measure on boundaries of strictly pseudoconvex
domains in $\mathbb{C}^2$. In particular, it is shown that Fefferman's measure
can be recovered from the Bergman kernel of the domain. A connection with the
geometry of the Heisenberg group, emerging from these results, is also
discussed.
