  The main results of this paper consists of two parts. Firstly, we obtain an
almost rigidity theorem which says that on a RCD(0, N) space, when a domain
between two level sets of a distance function has almost maximal volume
compared to that of a cylinder, then this portion is close to a cylinder as a
metric space. Secondly, we apply this almost rigidity theorem to study
noncompact RCD(0, N) spaces with linear volume growth. More precisely, we
obtain the sublinear growth of diameter of geodesic spheres, and study the
non-existence of harmonic functions with polynomial growth on such RCD(0,N)
spaces.
