On the (p,q)$(p,q)$-type strong law of large numbers for sequences of independent random variables |
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Authors: | Lê Vǎn Thành |
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Institution: | Department of Mathematics, Vinh University, Nghe An, Vietnam |
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Abstract: | Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 368 (2016), no. 1, 539–561) introduced a refinement of the Marcinkiewicz–Zygmund strong law of large numbers (SLLN), the so-called -type SLLN, where and . They obtained sets of necessary and sufficient conditions for this new type SLLN for two cases: , , and . Results for the case where and remain open problems. This paper gives a complete solution to these problems. We consider random variables taking values in a real separable Banach space , but the results are new even when is the real line. Furthermore, the conditions for a sequence of random variables -type SLLN are shown to provide an exact characterization of stable type p Banach spaces. |
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Keywords: | complete convergence in mean (p q)$(p q)$-type strong law of large numbers real separable Banach space stable type p Banach space strong law of large numbers |
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