  We shall prove a convergence result relative to sequences of Minkowski
symmetrals of general compact sets. In particular, we investigate the case when
this process is induced by sequences of subspaces whose elements belong to a
finite family, following the path marked by Klain in [13], and the
generalizations in [4] and [2]. We prove an analogue result for Fiber
symmetrization of a specific class of compact sets. The idempotency for
symmetrization of this family of sets is investigated, leading to a simple
generalization of a result from Klartag [14] regarding the approximation of a
ball through a finite number of symmetrizations, and generalizing an
approximation result in [9]
