Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generalized Typicality for Abstract Alphabets   A new notion of typicality for arbitrary probability measures on standard
Borel spaces is proposed, which encompasses the classical notions of weak and
strong typicality as special cases. Useful lemmas about strong typical sets,
including conditional typicality lemma, joint typicality lemma, and packing and
covering lemmas, which are fundamental tools for deriving many inner bounds of
various multi-terminal coding problems, are obtained in terms of the proposed
notion. This enables us to directly generalize lots of results on finite
alphabet problems to general problems involving abstract alphabets, without any
complicated additional arguments. For instance, quantization procedure is no
longer necessary to achieve such generalizations. Another fundamental lemma,
Markov lemma, is also obtained but its scope of application is quite limited
compared to others. Yet, an alternative theory of typical sets for Gaussian
measures, free from this limitation, is also developed. Some remarks on a
possibility to generalize the proposed notion for sources with memory are also
given.

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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: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: adap-org