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Set theoretic real analysis. (English) Zbl 0901.26001

The article has a survey character. It deals with some results and problems concerning functions \(f: \mathbb{R}^n\to\mathbb{R}\) whose solutions or statements involve the use of set theory. The choice of the topics can be characterized by key words and phrases: Fubini theorem, continuous images, continuous restrictions, continuum hypothesis, Martin’s axiom, Blumberg theorem, symmetric continuity, Peano curve, Darboux functions, cardinal functions, addition of functions, derivatives, extensions of measure. Results are given without proofs and some open problems are presented.

MSC:

26-02 Research exposition (monographs, survey articles) pertaining to real functions
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
54-02 Research exposition (monographs, survey articles) pertaining to general topology
28-02 Research exposition (monographs, survey articles) pertaining to measure and integration
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