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On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions |
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| Authors: | Lech Maligranda Volodymyr V Mykhaylyuk |
| Institution: | a Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden b Department of Applied Mathematics, Chernivtsi National University, Kotsyubyn'skoho 2, 58012 Chernivtsi, Ukraine c Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland |
| Abstract: | A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view. |
| Keywords: | Absolutely continuous functions Lipschitz functions Superpositions Absolutely continuous functions of two variables Embeddings Strictly singular embeddings Superstrictly singular embeddings Beppo Levi spaces Sobolev spaces Rearrangement invariant spaces |
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