The entropy power of a sum is fractionally superadditive

It is shown that the entropy power of a sum of independent random vectors, seen as a set function, is fractionally superadditive. This resolves a conjecture of the first author and A. R. Barron, and implies in particular all previously known entropy power inequalities for independent random variables. It is also shown that, for general dimension, the entropy power of a sum of independent random vectors is not supermodular.

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