Characterizations of k-rectifiability in homogeneous groups

A well known notion of k-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of Rk. We prove some characterizations of k-rectifiability, when the metric space is an arbitrary homogeneous group. In particular, we show that the a.e. existence of the (k,G)-approximate tangent group implies k-rectifiability.