A tranversality theorem for holomorphic mappings and stability of Eisenman-Kobayashi measures

We show that Thom's Transversality Theorem is Valid for holomorphic mappings 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 analytic subset A of the jet space J(k)(S, M), f can be approximated in neighborhoods of compacts by holomorphic mappings whose k-jet extensions are transversal to A. As an application the stability of Eisenman-Kobayshi intrinsic k-measures with respect to deleting analytic subsets of codimension > k is proven. This is a generalization of the Campbell-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistances.