6533b829fe1ef96bd128abfd

RESEARCH PRODUCT

Images and Preimages of Null Sets

Pekka KoskelaStanislav Hencl

subject

Distortion (mathematics)Sobolev spaceSet (abstract data type)Null setPure mathematicsNull (mathematics)Type (model theory)Natural classCounterexampleMathematics

description

In this chapter we study conditions that guarantee that our mapping maps sets of measure zero to sets of measure zero. We start with the problem in general Sobolev spaces, after which we establish a better result for mappings of finite distortion. Then we introduce a natural class of counterexamples to statements of this type and finally we give a weak condition under which the preimage of a set of measure zero has measure zero for mappings of finite distortion.

yearjournalcountryeditionlanguage
2013-11-20
https://doi.org/10.1007/978-3-319-03173-6_4