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Going beyond variation of sets
We study integralgeometric representations of variations of general sets A ? Rn without any regularity assumptions. If we assume, for example, that just one partial derivative of its characteristic function ?A is a signed Borel measure on R n with finite total variation, can we provide a nice integralgeometric representation of this variation? This is a delicate question, as the Gauss-Green type theorems of De Giorgi and Federer are not available in this generality. We will show that a ‘measure-theoretic boundary’ plays its role in such representations similarly as for the sets of finite variation. There is a variety of suitable notions of ‘measure theoretic boundary’ and one can address the question to find notions of measure-theoretic boundary that are as fine as possible.
History
Publication status
- Published
File Version
- Accepted version
Journal
Nonlinear Analysis: Theory, Methods and ApplicationsISSN
0362-546XPublisher
ElsevierExternal DOI
Volume
153Page range
230-242Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2016-11-18First Open Access (FOA) Date
2017-11-23First Compliant Deposit (FCD) Date
2016-11-18Usage metrics
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