Abstract
A result due to Gut asserts that the Marcinkiewicz–Zygmund strong law of large numbers for real-valued random variables is an amart a.s. convergence property. In this paper, a necessary and sufficient condition is given, under which that SLLN is also a quasimartingale. We also study the case of Banach-space valued r.v. and show that the scalar result remains true when the space is of suitable stable type.
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