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Measure Convex and Measure Extremal Sets

Published online by Cambridge University Press:  20 November 2018

Petr Dostál ,
Jaroslav Lukeš  and
Jiří Spurný
Petr Dostál
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic e-mail: dostal@karlin.mff.cuni.cz e-mail: lukes@karlin.mff.cuni.cz e-mail: spurny@karlin.mff.cuni.cz
Jaroslav Lukeš
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic e-mail: dostal@karlin.mff.cuni.cz e-mail: lukes@karlin.mff.cuni.cz e-mail: spurny@karlin.mff.cuni.cz
Jiří Spurný
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic e-mail: dostal@karlin.mff.cuni.cz e-mail: lukes@karlin.mff.cuni.cz e-mail: spurny@karlin.mff.cuni.cz
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Abstract

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We prove that convex sets are measure convex and extremal sets are measure extremal provided they are of low Borel complexity. We also present examples showing that the positive results cannot be strengthened.

Keywords

46A5552A07measure convex setmeasure extremal setface
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 4 , 01 December 2006 , pp. 536 - 548
Copyright
Copyright © Canadian Mathematical Society 2006

References

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