**MSC:**- 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.), See also {30E15}
- 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)

an asymptotic expansion is derived. Based upon a geometric measure

representation for the Gaussian law the interactions between global

and local geometric properties both of the distribution and of the

large deviation domain are studied. The advantage of the result is

that the expansion coefficients can be obtained by making a series

expansion of a surface integral avoiding the calculation of higher

order derivatives.