Joachim Naumann
,
Christian Simader
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 43
MSC 2000
- 28A75 Length, area, volume, other geometric measure theory
-
58C35 Integration on manifolds; measures on manifolds
Abstract
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 ${\cal L}({\cal M}^k)$.
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