A remark about Laczkovich's theorem on functions whose sections are derivatives (Q1094546)
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scientific article; zbMATH DE number 4025740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark about Laczkovich's theorem on functions whose sections are derivatives |
scientific article; zbMATH DE number 4025740 |
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A remark about Laczkovich's theorem on functions whose sections are derivatives (English)
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1987
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\textit{M. Laczkovich} [Period. Math. Hung. 12, 243-254 (1981; Zbl 0449.26009)] has proved that each real function of two real variables all of whose sections in both coordinates are derivatives, is Lebesgue measurable. In this paper, the author constructs a real function of two real variables which is not Lebesgue measurable and all of whose sections of the function in both coordinates belong to the Preiss class \(M^*_ 3\) [\textit{D. Preiss}, Trans. Am. Math. Soc. 272, 161-184 (1982; Zbl 0508.26001)].
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nonmeasurable functions
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Zahorski classes
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Lebesgue measurable functions
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sections of functions of two variables
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Preiss class \(M^ *_ 3\)
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