Search results for "Borel equivalence relation"

showing 2 items of 2 documents

A space on which diameter-type packing measure is not Borel regular

1999

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.

CombinatoricsBorel equivalence relationRiesz–Markov–Kakutani representation theoremApplied MathematicsGeneral MathematicsRadon measureStandard probability spaceBaire measureBorel setBorel measureMeasure (mathematics)MathematicsProceedings of the American Mathematical Society
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A Note on Algebraic Sums of Subsets of the Real Line

2002

AbstractWe investigate the algebraic sums of sets for a large class of invari-ant ˙-ideals and ˙- elds of subsets of the real line. We give a simpleexample of two Borel subsets of the real line such that its algebraicsum is not a Borel set. Next we show a similar result to Proposition 2from A. Kharazishvili paper [4]. Our results are obtained for ideals withcoanalytical bases. 1 Introduction We shall work in ZFC set theory. By !we denote natural numbers. By 4wedenote the symmetric di erence of sets. The cardinality of a set Xwe denoteby jXj. By R we denote the real line and by Q we denote rational numbers. IfAand Bare subsets of R n and b2R , then A+B= fa+b: a2A^b2Bgand A+ b= A+ fbg. Simila…

Discrete mathematicsRational numberLebesgue measurenull setsBaire propertyMathematics::LogicBorel equivalence relation03E15Borel setsalgebraic sumsPolish spaceGeometry and TopologyProperty of Baire26A21Borel setBorel measureReal line28A05AnalysisDescriptive set theoryMathematicsReal Analysis Exchange
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