Abstract
IfB is a weakly compactly generated Banach space andf: (S,S, μ) satisfies the strong law of large numbers, thenf=f 1+f 2, wheref 1 is Bochner μ-integrable andf 2 is Pettis μ-integrable with Pettis norm 0. The decomposition is unique.
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Dobrić, V. Weakly compactly generated Banach spaces and the strong law of large numbers. J Theor Probab 7, 129–134 (1994). https://doi.org/10.1007/BF02213363
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DOI: https://doi.org/10.1007/BF02213363