Let be a nilpotent orbit for a semisimple Lie group which appears as the leading orbit in the wave-front set of an -module. We establish a limit formula for the computation of the canonical measure on through differentiation of the canonical measures on elliptic orbits.
"A limit formula for elliptic orbital integrals." Duke Math. J. 113 (2) 331 - 353, 1 June 2002. https://doi.org/10.1215/S0012-7094-02-11325-8