Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lukacs theorem and the Olkin-Baker equation   The Olkin-Baker functional equation is closely related to the celebrated
Lukacs characterization of the gamma distribution. Its deeper understanding is
essential to settle a challenging question of multivariate extensions of the
Lukacs theorem. In this paper, first, we provide a new approach to the additive
Olkin-Baker equation which holds almost everywhere on (0,\infinity)^2 (with
respect to the Lebesgue measure on R^2) under measurability assumption. Second,
this new approach is adapted to the case when unknown functions are allowed to
be non-measurable and the complete solution is given in such a general case.
Third, the Olkin-Baker equation holding outside of a set from proper linearly
invariant ideal of subsets of R^2 is considered.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: hep-th