2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219969This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds in this setting.35 pagesProbabilityDifferential Geometry60J65 28D05 (Primary); 58J65 22E65 (Secondary)text