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a.e. n n absolutely summing operators amart convergence theorem asymptotic martingales ba(F Banach lattice Banach space Bellow bounded amarts bounded linear operator bounded martingales bounded stopping bounded variation bounded vector bva(F C.R. Acad Chacon characterization cone absolutely summing Corollary decomposition for W-bounded Doob potential Edgar and Sucheston Egghe Example exists following are equivalent Gebiete Ghoussoub hence holds isomorphic KB-space L^-bounded Lebesgue decomposition Lemma limit measure Math Multivariate Anal norm Notes in Mathematics order amarts order complete order continuous order potentials Paris SÚrie pointwise convergence Proof Radon-Nikodym derivatives Radon-Nikodym property random variables Riesz decomposition Section semiamart sequence set function process stochastic basis stochastic processes strong amarts supermartingale Suppose IE T-bounded set function T-norm topological vector lattice Tulcea uniform amart uniform potential uniform weak amart uniformly integrable uT(Q vector measure vector-valued W-bounded submartingale w-lim Wahrscheinlichkeitstheorie verw weak convergence weak sequential amarts weakly yields