The ell_p norms enjoy the following property : || x \otimes y || = ||x|| . ||y||

We prove that this property characterizes ell_p norms among permutation-invariant norms on the space of finitely supported sequences.

The proof is based on the tensor power trick together with Cramér's large deviations theorem.

Here is a blog post at the n-Category Café where Tom Leinster reformulates our result in a slightly different form.

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aubrun
(arrobas) math. univ-lyon1. fr