Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance-like functions and smooth approximations: a correction to
  "Logarithm laws for flows on homogeneous spaces"   One of the propositions in the paper [D. Kleinbock and G.A. Margulis,
Logarithm laws for flows on homogeneous spaces, Invent. Math. 138 (1999),
451-494] related to approximating certain sets by smooth functions, was
recently found to be incorrect. Here we correct the mistake.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph