Integration of a Differential Form on an Analytic Complex Subvariety.

for an exterior differential form so on an analytic complex subvariety W. The problem arises because an analytic complex subvariety in a domain D of Cn (or, more briefly, an analytic set in D) is not, in general, a manifold. We give (a) an existence theorem for t(p) and (b) a proof that t is a closed current in D, that is, t(4b) = 0 for the forms 41 with compact support, which are homologous to zero in D. II. A set W is called an analytic set in a domain D of Cn(zl, ..., zn) if M e D has a neighborhood (UM) such that (UM) n W is defined by the simultaneous equations