Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nearest Neighbor Characterization of Lebesgue Points in Metric Measure
  Spaces   The property of almost every point being a Lebesgue point has proven to be
crucial for the consistency of several classification algorithms based on
nearest neighbors. We characterize Lebesgue points in terms of a 1-Nearest
Neighbor regression algorithm for pointwise estimation, fleshing out the role
played by tie-breaking rules in the corresponding convergence problem. We then
give an application of our results, proving the convergence of the risk of a
large class of 1-Nearest Neighbor classification algorithms in general metric
spaces where almost every point is a Lebesgue point.

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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con