...Ciesielski
The author wishes to thank Professors Lee Larson, Marek Balcerzak, Andy Bruckner, Tomasz Natkaniec, Juris Steprans, and Brian Thomson for reading preliminary versions of this paper and helping in improving its final version. 
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...countable.
This approach was used in the paper [125], while the Luzin set approach in the paper [126]. Since they are published in the same year, the priority is not completely clear. However in the list of Sierpinski's publications printed in [130] paper [125] precedes [126], suggesting its priority. 
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...countable.
The construction of such a set, under CH, was published by Luzin in 1914 [93]. The same construction had been also published in 1913 by Mahlo [95]. But (as is not unusual in mathematics) such a set is commonly known as a Luzin set. 
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...form
Co-countable symmetric derivatives are replaced by co-tex2html_wrap_inline260 symmetric derivatives and the theorem is proved in ZFC. 
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...function.
In fact, a Hamel basis tex2html_wrap_inline262 can be chosen to be both first category and measure zero. Thus tex2html_wrap_inline264 can be measurable and have the Baire property. 
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...NAME="thCMPS">
Recall that for tex2html_wrap_inline266 if there exists an tex2html_wrap_inline270 such that tex2html_wrap_inline272 for every m>n. 
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...NAME="propCRec">
In [41] (4) was proved with the additional assumption that tex2html_wrap_inline276. This extra assumption was removed by F. Jordan in [69]. 
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...NAME="thJor2">
The first equation from part (4) was proved by K. Ciesielski. 
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...way.
See also 1969 paper of Mrówka [103] on characterizing functions by associated sets. 
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...in [#C##1#].
According to [113] already in a 1988 manuscript [137] Tartaglia proved that the class of all derivatives cannot be topologized. 
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