Search results for "null sets"

showing 3 items of 3 documents

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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Differentiability of Lipschitz maps

2010

Lipschitz maps Gateaux-differentiability null sets in Banach spaces.
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A decomposition theorem for σ-P-directionally porous sets in Fréchet spaces

2007

In this paper we study suitable notions of porosity and directional porosity in Fréchet spaces. Moreover we give a decomposition theorem for $\sigma$-$\mathcal{P}$-directionally porous sets.

Settore MAT/05 - Analisi Matematicalcsh:MathematicsDifferentiability of Lipschitz maps null setslcsh:QA1-939
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