Random series in  using unconditional basic sequences and  stable sequences: A result on almost sure almost everywhere convergence |
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| Authors: | Juan M. Medina B. Cernuschi-Frí as |
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| Affiliation: | Facultad de Ingeniería, Paseo Colón 850 (1063), Capital Federal, Depto. de Mathemática, Universidad de Buenos Aires and Instituto Argentino de Matemática, Conicet, Argentina ; Facultad de Ingeniería, Universidad de Buenos Aires and Instituto Argentino de Matemática, Conicet, Argentina |
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| Abstract: | Here we study the almost sure almost everywhere convergence of random series of the form  in the Lebesgue spaces  , where the  's are centered random variables, and the  's constitute an unconditional basic sequence or an  stable sequence. We show that if one of these series converges in the norm topology almost surely, then it converges almost everywhere almost surely. |
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| Keywords: | Unconditional basic sequence almost sure convergence random series. |
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