ON STRONG CONVERGENCE OF PRAMARTS IN BANACH SPACES
Abstract: We present new versions of strong convergence results for Banach-space-valued pramarts
based on various tightness conditions combined with uniform integrability conditions of
Mazur type. They extend a result of Egghe [7] stating that every Banach-space-valued
pramart with a Cesŕro-mean convergent subsequence converges strongly almost surely.
Similar results are obtained for pramarts with values in the dual of a separable Banach space.
2000 AMS Mathematics Subject Classification: Primary: 60B11, 60B12,
60G48.
Keywords and phrases: Pramart, conditional expectation, tightness conditions, strong
convergence, -measurable function, Lé vy’s theorem.