# Nullset-preserving map

From Diffgeom

## Definition

Let and be differential manifolds. A map (not necessarily smooth) is termed **nullset-preserving** if has measure zero if and only if has measure zero.

Any diffeomorphism is nullset-preserving. In fact, it is because we have this fact for Euclidean space that we can define the notion of a nullset on a differential manifold to begin with. `Further information: Diffeomorphism implies nullset-preserving`