2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75050A 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.Some errors and misprints corrected; new references have been addedProbabilityClassical Analysis and ODEs60F-xx; 43A35text