A TRANVERSALITY THEOREM FOR HOLOMORPHIC MAPPINGS AND STABILITY OF EISENMAN-KOBAYASHI MEASURES

We show that Thom's Transversality Theorem is Valid for holomorphic ma ppings from Stein manifolds. More precisely, given such a mapping f : S --> M from a Stein manifold S to a complex manifold M and given an a nalytic subset A of the jet space J(k)(S, M), f can be approximated in neighborhoods of compacts by holomorphic mappings whose k-jet extensi ons are transversal to A. As an application the stability of Eisenman- Kobayshi intrinsic k-measures with respect to deleting analytic subset s of codimension > k is proven. This is a generalization of the Campbe ll-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistanc es.