Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the pointwise domination of a function by its maximal function   We show that under rather general circumstances, the almost everywhere
pointwise inequality $|f|(x) \le Mf (x)$ is equivalent to a weak form of the
Lebesgue density theorem, for totally bounded closed sets. We derive both
positive and negative results from this characterization.

4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: stat