2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115508It is proved that generalized excursion measures can be constructed via time change of Ito's Brownian excursion measure. A tightness-like condition on strings is introduced to prove a convergence theorem of generalized excursion measures. The convergence theorem is applied to obtain a conditional limit theorem, a kind of invariance principle where the limit is the Bessel meander.20 pages. Dedicated to Professor M. Fukushima on the occasion of his 70th birthdayProbability60J25; 60F17text