  In this note, we study B{\'e}zout type inequalities for mixed volume and
Minkowski sum of convex bodies in R n. We first give a new proof and we extend
inequalities of Jian Xiao on mixed discriminants. Then, we use mass transport
method to deduce some B{\'e}zout type inequalities for mixed volumes. Finally,
we apply these inequalities to obtain B{\'e}zout type inequalities for
Minkowski sums.
