  A classical theorem of S. Bochner states that a function
  $f:R^n \to C$ is the Fourier transform of a finite Borel measure if and only
if $f$ is positive definite. In 1938, I. Schoenberg found a beautiful
complement to Bochner's theorem.
  We present a non-technical derivation of of Schoenberg's theorem that relies
chiefly on the de Finneti theorem and the law of large numbers of classical
probability theory.
