  The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a
powerful tool with many applications to singular integrals, ergodic theory, and
spectral theory of operators. Transference methods afford a unified approach to
many problems in diverse areas, which before were proved by a variety of
methods. The purpose of this paper is to bring about a similar approach to the
study of measures. Specifically, deep results in classical harmonic analysis
and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others,
are all extensions of the classical F.&M. Riesz Theorem. We will show that all
these extensions are obtainable via our new transference principle for spaces
of measures.
