Measure and Integration on Lipschitz-Manifolds

The first part of this paper is concerned with various definitions of a $k$-dimensional Lipschitz manifold ${\cal M}^k$ and a discussion of the equivalence of these definitions. The second part is then devoted to the geometrically intrinsic construction of a $\sigma$-algebra ${\cal L}({\cal M}^k)$ of subsetsof ${\cal M}^k$ and a measure $\mu_k$ on ${\cal L}({\cal M}^k)$