  We express the Segre class of a monomial scheme -- or, more generally, a
scheme monomially supported on a set of divisors cutting out complete
intersections -- in terms of an integral computed over an associated body in
euclidean space. The formula is in the spirit of the classical
Bernstein-Kouchnirenko theorem computing intersection numbers of equivariant
divisors in a torus in terms of mixed volumes, but deals with the more refined
intersection-theoretic invariants given by Segre classes, and holds in the less
restrictive context of `r.c. monomial schemes'.
