  The goal of this note is to prove the Half Space Property for $RCD(0,N)$
spaces, namely that if $(X,d,m)$ is a parabolic $RCD(0,N)$ space and $ C
\subset X \times \mathbb{R}$ is locally the boundary of a locally perimeter
minimizing set and it is contained in a half space, then $C$ is a locally
finite union of horizontal slices. If the assumption of local perimeter
minimizing is strengthened into global perimeter minimizing, then the
conclusion can be strengthened into uniqueness of the horizontal slice. As a
consequence, we obtain oscillation estimates and a Half Space Theorem for
minimal hypersurfaces in products $M \times \mathbb{R}$, where $M$ is a
parabolic smooth manifold (possibly weighted and with boundary) with
non-negative Ricci curvature. On the way of proving the main results, we also
obtain some properties of Green's functions on $RCD(K,N)$ spaces that are of
independent interest.
