  We prove a generalization to the context of real geometry of an intersection
formula for the vanishing cycle functor, which in the complex context is due to
Dubson, Ginsburg, Le and Sabbah (after a conjecture of Deligne). It is also a
generalization of similar results of Kashiwara-Schapira, where these authors
work with a suitable assumption about the micro-support of the corresponding
constructible complex of sheaves. We only use a similar assumption about the
support of the corresponding characteristic cycle so that our result can be
formulated in the language of constructible functions and Lagrangian cycles.

Algebraic Geometry;Complex Variables