2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60913We show that for stochastic measures with freely independent increments, the partition-dependent stochastic measures of math.OA/9903084 can be expressed purely in terms of the higher stochastic measures and the higher diagonal measures of the original.15 pages, AMS-LaTeX2e. A serious revision following the suggestions by the refereeOperator AlgebrasCombinatoricsProbability46L54 (Primary) 60G, 60H (Secondary)text