A note on lp-norms

Abstract.

Let x ₁,..., x _n and y ₁,..., y _n be nonnegative numbers. If the l ^p-norm of (x ₁,..., x _n ) coincides with that of (y ₁,..., y _n ) for n different values of p > 0, then the x _i are a permutation of the x _i. This generalizes a well-known algebraic result which concerns the exponents p = 1,..., n.¶Some consequences as well as some generalizations to infinite sequences and to functions are also discussed.