  Let G be a connected reductive group defined over a non-archimedean local
field of characteristic 0. We assume G is quasi-split, adjoint and absolutly
simple. Let g be the Lie algebra of G. We consider the space of the invariant
distributions on g(F), which are stable and supported by the set of nilpotent
elements of g(F). Magdy Assem has stated several conjectures which describe
this space. We prove some of these conjectures, assuming that the residual
characteristic of F is "very large" relatively to G.
