On the Lp convergence of sums of independent random variables
- 1 November 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 82 (3) , 439-446
- https://doi.org/10.1017/s0305004100054104
Abstract
Let {Xnj, 1 ≤ j ≤ kn} be independent random variables with zero means and satisfying . Let p ≥ 1. We prove thatif and only if, for all ε > 0,and we use this result to obtain necessary and sufficient conditions for the Lp convergence of sums of non-negative, independent random variables.Keywords
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