original_query: What is the Brunn-Minkowski theorem in mathematics?
query: What is the Brunn-Minkowski theorem in mathematics?
answer: The Brunn-Minkowski theorem (or inequality) relates the volumes of compact subsets of Euclidean space.  The original version applied to convex sets, but it's been generalized to compact non-convex sets.  It states that for non-empty compact subsets A and B of Rⁿ,  μ(A + B)^(1/n) ≥ μ(A)^(1/n) + μ(B)^(1/n), where μ is the Lebesgue measure and A + B is the Minkowski sum.