Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measurability Aspects of the Compactness Theorem for Sample Compression
  Schemes   It was proved in 1998 by Ben-David and Litman that a concept space has a
sample compression scheme of size d if and only if every finite subspace has a
sample compression scheme of size d. In the compactness theorem, measurability
of the hypotheses of the created sample compression scheme is not guaranteed;
at the same time measurability of the hypotheses is a necessary condition for
learnability. In this thesis we discuss when a sample compression scheme,
created from com- pression schemes on finite subspaces via the compactness
theorem, have measurable hypotheses. We show that if X is a standard Borel
space with a d-maximum and universally separable concept class C, then (X,C)
has a sample compression scheme of size d with universally Borel measurable
hypotheses. Additionally we introduce a new variant of compression scheme
called a copy sample compression scheme.

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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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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: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph