Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Luzin and Sierpi\'nski sets, some nonmeasurable subsets of the plane and
  additive properties on the line   In this paper we shall introduce some nonmeasurable and completely
nonmeasurable subsets of the plane with various additional properties, e.g.
being Hamel basis, intersecting each line in a strong Luzin / Sierpi\'nski set.
Also some additive properties of Luzin and Sierpi\'nski sets and their
generalization I-Luzin sets, on the line are investigated.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: chem-ph