Let F be a non-Archimedean local field with ring of integers R and prime ideal $\frak p$. Suppose T is a GLn(F)-invariant distribution on ${\frak g}$=Mn(F), the Lie algebra of GLn(F). If T has support in the set of topologically nilpotent elements, then the restriction of T to the set of functions which are compactly supported and invariant under Mn($\frak p$) may be expressed as a linear combination of nilpotent orbital integrals restricted to the same set of functions.