Search results for "Measurable set"

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Integration of both the derivatives with respect to P-paths and approximative derivatives

2009

In the present paper, in terms of generalized absolute continuity, we present a descriptive characteristic of the primitive with respect to a system of P-paths and study the relationship between the Denjoy-Khinchin integral and the Henstock H P-integral. © 2009 Pleiades Publishing, Ltd.

Pure mathematicsDenjoy-Khinchin integralMeasurable setGeneral MathematicsCalculusDerivative with respect to P-pathHenstock H P-integralMathematics (all)Absolute continuityAbsolute continuityBaire theoremMathematics
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Hamel-isomorphic images of the unit ball

2010

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Unit sphereDiscrete mathematicsRational numberUniversally measurable setBounded functionField (mathematics)IsomorphismReal lineUnit diskMathematicsMathematical Logic Quarterly
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