Mahler's inequality
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 "x", "y" > 0 for all "k". Proof. By the inequality of arithmetic and geometric means, we have: and Hence, Clearing denominators then gives the desired result.