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A NOTE ON SOME TOPOLOGICAL PROPERTIES OF SETS WITH FINITE PERIMETER

Part of: Classical measure theory

Published online by Cambridge University Press:  23 July 2015

SILVANO DELLADIO
SILVANO DELLADIO*
Affiliation:
University of Trento, Department of Mathematics, via Sommarive 14, 38123 Trento, Italy e-mail: delladio@science.unitn.it
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Abstract

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Some well-known results about the 2-density topology on ${\mathcal R}$ (in particular in the context of the Lusin–Menchoff property) are extended to τbm, i.e. the m-density topology on ${\mathcal R}$n with m ∈ (n,+∞). Every set of finite perimeter in ${\mathcal R}$n is equivalent (in measure) to a set in τbm0, where m0=n+1+${1\over n-1}$. There exists a set of finite perimeter in ${\mathcal R}$n which is not equivalent (in measure) to any member in the a.e.-modification of τbm, whatever m ∈ [n,+∞).

MSC classification

Primary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 637 - 647
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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