sentences:  Vitale's random Brunn–Minkowski inequality
  
  In mathematics, Vitale's random Brunn–Minkowski inequality is a theorem due to Richard Vitale that generalizes the classical Brunn–Minkowski inequality for compact subsets of "n"-dimensional Euclidean space R"n" to random compact sets.Let "X" be a random compact set in R"n"; that is, a Borel–measurable function from some probability space (Ω, Σ, Pr) to the space of non-empty, compact subsets of R"n" equipped with the Hausdorff metric.