2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79083This 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 Levy property. We then give a connection between the tail distribution and the pth moment, and between the pth moment and the rearrangement invariant norms.Also available at http://math.missouri.edu/~stephen/preprints/ProbabilityFunctional AnalysisPrimary 60G50, 60E15, 46E30; Secondary 46B09text