  In this note we analyze the relationship between the properties of von
Neumann-Morgenstern utility functions and expected utility functions. More
precisely, we investigate which of the regularity and concavity assumptions
usually imposed on the latter transfer to the former and vice versa. In
particular we obtain that, in order for the expected utility functions to
fulfill such classical properties, it is enough to assume them for the von
Neumann-Morgenstern utility functions.
