Null subset of a differential manifold

From Diffgeom
Revision as of 19:50, 18 May 2008 by Vipul (talk | contribs) (6 revisions)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search


Let M be a differential manifold. A subset S of M is said to have measure zero or to be a null subset if the following holds: for any open subset U of M and any diffeomorphism between U and \R^n, the image of U \cap S under the diffeomorphism has measure zero in \R^n.

The well-definedness of this notion rests on the fact that any diffeomorphism between open subsets of \R^n maps measure zero subsets to measure zero subsets (this is not true for arbitrary homeomorphisms, and hence the notion of a measure zero subset does not make sense for a topological manifold). Further information: Diffeomorphism implies nullset-preserving