Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distortion and Distribution of Sets under Inner Functions   It is a classical result that Lebesgue measure on the unit circle is
invariant under inner functions fixing the origin. In this setting, the
distortion of Hausdorff contents has also been studied. We present here similar
results focusing on inner functions with fixed points on the unit circle. In
particular, our results yield information not only on the size of preimages of
sets under inner functions, but also on their distribution with respect to a
given boundary point. As an application, we use them to estimate the size of
irregular points of inner functions omitting large sets. Finally, we also
present a natural interpretation of the results in the upper half plane.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con