  The classical Brunn-Minkowski inequality states that for $A_1,A_2\subset\R^n$
compact, $$ |A_1+A_2|^{1/n}\ge |A_1|^{1/n}+|A_2|^{1/n}\eqno(1) $$ where
$|\cdot|$ denotes the Lebesgue measure on $\R^n$. In 1986 V. Milman {\bf [Mil
1]} discovered that if $B_1$ and $B_2$ are balls there is always a relative
position of $B_1$ and $B_2$ for which a perturbed inverse of $(1)$ holds. More
precisely:\lq\lq{\sl There exists a constant $C>0$ such that for all $n\in\N$
and any balls $B_1,B_2\subset\R^n$ we can find a linear transformation
$u\colon\R^n\to\R^n$ with $|{\rm det}(u)|=1$ and
  $$|u(B_1)+B_2|^{1/n}\le C(|B_1|^{1/n}+|B_2|^{1/n})"$$}
  The aim of this paper is to extend this Milman's result to a larger class of
sets.
