2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152370The purpose of this paper is to describe some conjectures and results on the existence and uniqueness of invariant measures on formal completions of Kac-Moody groups and associated homogeneous spaces. Existence is rigorously established in all affine type cases.101 pages; this is an AMS-TEX file; the paper has been submitted to J. Funct. AnalFunctional AnalysisOperator AlgebrasInvariant measures for unitary forms of Kac-Moody groups, Parts I-IIItext