Brunn–Minkowski theorem

The Brunn–Minkowski theorem is a fundamental result in the theory of convex bodies in geometry, particularly in the field of measure theory and geometric analysis. It provides a profound connection between the geometry of sets in Euclidean space and their measures (e.g., volumes). ### Statement of the Theorem: Let \( A \) and \( B \) be two non-empty, compact subsets of \( \mathbb{R}^n \) with positive measure.