2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161663We solve the moment problem for convex distribution functions on $[0,1]$ in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconis and Freedman, and relates this work to the Lévy-Khintchine formula for the Laplace transform of a subordinator, and to regenerative composition structures.Published in at http://dx.doi.org/10.1214/193940307000000374 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G09, 44A60 (Primary) 62E10 (Secondary)text