The decomposition theorem for functions satisfying the law of large numbers |
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| Authors: | V Dobric |
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| Institution: | (1) Department of Mathematics, Lehigh University, Christmas-Saucon Hall #14, 18015 Bethlehem, Pennsylvania |
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| Abstract: | LetB be a Banach space with the Radon-Nikodym property and (S,  ,  ) a probability space. Then anf: S B satisfies the strong law of large numbers if and only if there exists a Bochner integrable functionf
1 and a Pettis integrable functionf
2,f
2 f
2=0 in the Glivenko-Cantelli norm, such thatf=f
1+f
2. The composition is unique. |
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| Keywords: | Banach spaces with the Radon-Nikodym property the strong law of large numbers compact operators |
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