Vol. 67, No. 1, 1976

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Orlicz space convergence of martingales of Radon-Nikodým derivatives given a σ-lattice

David Alan Legg

Vol. 67 (1976), No. 1, 209–214

Let {Mk} be an increasing sequence of sub σ-lattices of a σ-algebra 𝒜, and let M be the σ-lattice generated by kMk. Let LΦ be an associated Orlicz space of 𝒜-measurable functions, where Φ does not necessarily satisfy the Δ2-condition. Given h LΦ, let fk be the Radon-Nikodym derivative of h given Mk. Necessary and sufficient conditions are given on h to insure that {fk} converges in LΦ to f, where f is the Radon-Nikodym derivative of h given M. The situation where f is valued in a Banach space with basis is also examined.

Mathematical Subject Classification
Primary: 60G45, 60G45
Received: 5 May 1976
Published: 1 November 1976
David Alan Legg