Mathematics – Probability
Scientific paper
2005-04-29
Mathematics
Probability
Some errors and misprints corrected; new references have been added
Scientific paper
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.
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