### Abstract

We construct a metric space of set functions (script Q sign(script X sign), d) such that a sequence {P_{n}} of Borel probability measures on a metric space (script X sign, d*) satisfies the full Large Deviation Principle (LDP) with speed {a_{n}} and good rate function I if and only if the sequence {P^{an}_{n}} converges in (script Q sign(script X sign), d) to the set function e^{-I}. Weak convergence of probability measures is another special case of convergence in (script Q sign(script X sign), d). Properties related to the LDP and to weak convergence are then characterized in terms of (script Q sign(script X sign), d).

Original language | English (US) |
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Pages (from-to) | 805-824 |

Number of pages | 20 |

Journal | Journal of Theoretical Probability |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - 2000 |

### Keywords

- Large deviations
- Metric spaces

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## Cite this

Jiang, T., & O'Brien, G. L. (2000). The Metric of Large Deviation Convergence.

*Journal of Theoretical Probability*,*13*(3), 805-824. https://doi.org/10.1023/A:1007814729591