Null subset of a differential manifold
Let be a differential manifold. A subset of is said to have measure zero or to be a null subset if the following holds: for any open subset of and any diffeomorphism between and , the image of under the diffeomorphism has measure zero in .
The well-definedness of this notion rests on the fact that any diffeomorphism between open subsets of 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