Homogeneity of Certain Invariant Distributions on the Lie Algebra of p-adic GLn

Let F be a non-Archimedean local field with ring of integers R and prime ideal . Suppose T is a GL_n(F)-invariant distribution on =M_n(F), the Lie algebra of GL_n(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 M_n() may be expressed as a linear combination of nilpotent orbital integrals restricted to the same set of functions.