2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74735We show that the set of max-plus measures representing a given max-plus harmonic vector has a least element. This may be viewed as an analogue of the uniqueness of the integral representation of harmonic functions in Potential Theory. As an application, we show how the distance-like functions of a metric space can be expressed in terms of the Busemann points of the metric boundary.15 pages, 0 figuresMetric GeometryOptimization and Control53C23 (Primary) 47J10 49L20 (Secondary)text