LP-CONVERGENCE OF A CERTAIN CLASS OF PRODUCT MARTINGALES

We establish the Kakutani dichotomy property for two generalized Rademacher-Riesz product measures mu, nu; that either mu, nu are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon-Nikodym derivative du/dv belongs to L(p)(nu) for all positive real numbers p, by proving that a certain product martingale converges in L(p)(nu) for p greater-than-or-equal-to 1.