  This paper is devoted to the proof Gauss' divergence theorem in the framework
of "ultrafunctions". They are a new kind of generalized functions, which have
been introduced recently [2] and developed in [4], [5] and [6]. Their
peculiarity is that they are based on a non Archimedean field namely on a field
which contains infinite and infinitesimal numbers. Ultrafunctions have been
introduced to provide generalized solutions to equations which do not have any
solutions not even among the distributions.
