Generic properties of function spaces have been of particular interest in dynamical systems and singularity theory. The underlying assumption has been that the complement of a dense G δ {G_\delta } set is sparse enough to be considered unlikely. Nevertheless, in infinite dimensional spaces, even dense G δ {G_\delta } ’s may have measure zero. Since there is no one canonical measure on an infinite dimensional Fréchet space, notions of measure zero have not often been considered. Here we use a notion of Haar measure zero on abelian Polish groups due to Christensen [1]. We show that those sections of a finite dimensional vector bundle over a compact manifold whose jets are transverse to a submanifold of the jet bundle are complements of sets of Haar measure zero.