L”-Convergence of a Certain Class of Product Martingales
Date
1994Source
Proceedings of the Edinburgh Mathematical SocietyVolume
37Issue
2Pages
243-254Google Scholar check
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We establish the Kakutani dichotomy property for two generalized Rademacher-Riesz product measures p, v that either p, v 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 dp/dv belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p 1. © 1994, Edinburgh Mathematical Society. All rights reserved.