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2010/2011 Upper Porosity With Respect to Measures
Martin Koc
Real Anal. Exchange 36(1): 91-106 (2010/2011).


For subsets of a separable metric space $X$ we introduce the notion of upper porosity with respect to a~Borel regular probabilistic measure $\mu$ on $X$ (called $\mu$-upper porosity) that generalizes the concept of upper porosity of the measure $\mu$. We explore several natural definitions and further provide a definition of even more general type of $\mu$-upper porosity given by suitable porosity functions. As the main consequence of achieved results concerning general $\mu$-upper porosities we get that every $\sigma$-$\mu$-upper porous set can be decomposed to a $\sigma$-strongly upper porous set and a $\mu$-null set.


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Martin Koc. "Upper Porosity With Respect to Measures." Real Anal. Exchange 36 (1) 91 - 106, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1246.28003
MathSciNet: MR3016406

Primary: 28A05 , 28A12

Keywords: generalized upper porosity , upper porosity , upper porosity of measures

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
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