  The behavior of the volume of the tube of distance r, around a given compact
set M, is an old and important question with relations to many fields, like
differential geometry, geometric measure theory, integral geometry, and also
probability and statistics. Federer (1959) introduces the class of sets with
positive reach, for which the volume is given by a polynom in r. For
applications, in numerical analysis and statistics for example, an almost
polynomial behavior is of equal interest. We exhibit an example showing how far
to a polynom can be the volume of the tube, for the simplest extension of the
class of sets with positive reach, namely the class of locally finite union of
sets with positive reach satisfying a tangency condition introduced by Zahle
(1984).
