Pawel Hitczenko and Stephen Montgomery-Smith, Measuring the magnitude of sums of independent random variables. Annals of Probability, 29, (2001), 447-466. This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Lévy property. We then give a connection between the tail distribution and the \(p\)th moment, and between the \(p\)th moment and the rearrangement invariant norms. (tex, dvi, ps, pdf, html.)


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