Mahler's inequality

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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[edit]

By the inequality of arithmetic and geometric means, we have:

and

Hence,

Clearing denominators then gives the desired result.

See also[edit]

References[edit]