### Abstract

This paper proposes a new notion of a typical sequence over an abstract alphabet based on approximation of memoryless sources by empirical distributions, uniformly over a class of measurable "test functions." In the finite-alphabet case, we can take all uniformly bounded functions and recover the usual notion of typicality under total variation distance. For a general alphabet, this function class is too large, and must be restricted. We develop our notion of typicality with respect to any Glivenko-Cantelli function class (which admits a Uniform Law of Large Numbers) and demonstrate its power by deriving fundamental limits on achievable rates in several settings that can be reduced to uniform approximation of general-alphabet memoryless sources with respect to a suitable function class.

Original language | English (US) |
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Title of host publication | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings |

Pages | 1458-1462 |

Number of pages | 5 |

DOIs | |

State | Published - Aug 23 2010 |

Externally published | Yes |

Event | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: Jun 13 2010 → Jun 18 2010 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8103 |

### Other

Other | 2010 IEEE International Symposium on Information Theory, ISIT 2010 |
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Country | United States |

City | Austin, TX |

Period | 6/13/10 → 6/18/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings*(pp. 1458-1462). [5513601] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2010.5513601