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## Abstract

Call a sequence {Xn} of r.v.'s ε-exchangeable if on the same probability space there exists an exchangeable sequence {Yn} such that P(|Xn -Yn|≧ε)≦ε for all n. We prove that any tight sequence {Xn} defined on a rich enough probability space contains ε-exchangeable subsequences for every ε>0. The distribution of the approximating exchangeable sequences is also described in terms of {Xn}. Our results give a convenient way to prove limit theorems for subsequences of general r.v. sequences. In particular, they provide a simplified way to prove the subsequence theorems of Aldous [1] and lead also to various extensions.

Original language | English |
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Pages (from-to) | 395-413 |

Journal | Probability theory and related fields |

Volume | 73 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1986 |

Externally published | Yes |

## Treatment code (Nähere Zuordnung)

- Basic - Fundamental (Grundlagenforschung)

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Dive into the research topics of 'Exchangeable random variables and the subsequence principle'. Together they form a unique fingerprint.## Projects

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