Really just the triangle inequality for p-norms: For any p>=1, a1,...,an≥0 and b1,...,bn≥0,

((a1+b1)p + ... + (an+bn)p)1/p ≤ (a1p+...+anp)1/p + (b1p+...+bnp)1/p

A version with integrals (instead of sums) exists too, of course.

A proof of Minkowski's inequality follows from some trickery with Hölder's inequality.

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