Abstract
In this work, we are concerned with the study of the N-Lusin property in metric measure spaces. A map satisfies that property if sets of measure zero are mapped to sets of measure zero. We prove a new sufficient condition for the N-Lusin property using a weak and pointwise Lipschitz-type estimate. Relations with approximate differentiability in metric measure spaces and other sufficient conditions for the N-Lusin property will be provided.
Funding source: Agencia Nacional de Promoción Científica y Tecnológica
Award Identifier / Grant number: PICT 1701-2015
Award Identifier / Grant number: SECTYP BO51
Funding statement: M. Garriga and P. Ochoa were partially supported by Grants PICT 1701-2015 and SECTYP BO51.
Acknowledgements
The authors would like to thanks the anonymous referee for her/his very useful comments and suggestions which have been helpful to improve the manuscript.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The Mackey problem for free locally convex spaces
- Restricted averaging operators to cones over finite fields
- Asymptotic expansion of holonomy
- Compactness criteria for real algebraic sets and Newton polyhedra
- Unit-graphs and special unit-digraphs on matrix rings
- ϕ-amenability and character amenability of Fréchet algebras
- Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
- Idempotence of finitely generated commutative semifields
- N-Lusin property in metric measure spaces: A new sufficient condition
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2. Part II
- Homogeneous Finsler spaces and the flag-wise positively curved condition
- Index of Grassmann manifolds and orthogonal shadows
- Jantzen filtration and strong linkage principle for modular Lie superalgebras
- On the maximum conjecture
Artikel in diesem Heft
- Frontmatter
- The Mackey problem for free locally convex spaces
- Restricted averaging operators to cones over finite fields
- Asymptotic expansion of holonomy
- Compactness criteria for real algebraic sets and Newton polyhedra
- Unit-graphs and special unit-digraphs on matrix rings
- ϕ-amenability and character amenability of Fréchet algebras
- Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
- Idempotence of finitely generated commutative semifields
- N-Lusin property in metric measure spaces: A new sufficient condition
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2. Part II
- Homogeneous Finsler spaces and the flag-wise positively curved condition
- Index of Grassmann manifolds and orthogonal shadows
- Jantzen filtration and strong linkage principle for modular Lie superalgebras
- On the maximum conjecture