In mathematics, Mahler's inequality, named after Kurt Mahler, states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means: when xk, yk > 0 for all k. Proof By the inequality of arithmetic and geometric means, we have: and Hence, Clearing denominators then gives the desired result. See also Minkowski inequality References Minkowski inequality in the Encyclopedia of Mathematics Inequalities Articles containing proofs