2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122305The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any 1-Lipschitz map $f$ from $X$ to a space $Y$ with a doubling measure also concentrates to a constant map. As a corollary, we get any 1-Lipschitz map to a Riemannian manifold with a lower Ricci curvature bounds also concentrates to a constant map.8pagesMetric Geometry28E99;53C23text