Abstract
The present book is based on the Zermelo-Fraenkel system of axioms of the Set Theory augmented by the axiom of choice. The axiom of choice plays a fundamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used.
R. M. Solovay has shown (Solovay [292]) that a model of mathematics (without axiom of choice) is possible in which all subsets of R (and consequently also all functions f : ℝ→ ℝ) are Lebesgue measurable.
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© 2009 Birkhäuser Verlag AG
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(2009). Set Theory. In: Gilányi, A. (eds) An Introduction to the Theory of Functional Equations and Inequalities. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8749-5_1
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DOI: https://doi.org/10.1007/978-3-7643-8749-5_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8748-8
Online ISBN: 978-3-7643-8749-5
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