  The Feynman path integral approach to quantum mechanics is examined in the
case where the configuration space is curved. It is shown how the ambiguity
that is present in the choice of path integral measure may be resolved if, in
addition to general covariance, the path integral is also required to be
consistent with the Schwinger action principle. On this basis it is argued that
in addition to the natural volume element associated with the curved space,
there should be a factor of the Van Vleck-Morette determinant present. This
agrees with the conclusion of an approach based on the link between the path
integral and stochastic differential equations.
