### Abstract

Let X,*., X be i.i.d. r. v.'s defined on the _{r} _{ct}probability space (X. A, P _), where 0 £0 is an open sub~ k ° set of 3R, k1 ; (ocl, n1, is a nondecreasiny sequence n of positive integers tending to _{00} as Let {x}, n1, be a sequence of positive real numbers tending to _{00} as n°°, and set 0_{T}=0+h 1, h£3R, hO. Finally, let P_{a}_{Q} ‘ n n _{1} _{n}, 0 ry-jj _{f} _{and}P ‘ be the restrictions of the urobability measu-n, 0 p _{1} _{res} P_{Q} and P_{p}t, respectively, to the a-fie1d A - an ‘n a(X,…, X)„ Then a necessary and sufficient condiantion for the sequences {P _{Q}} and {P ‘ } to be contin,0 n,0 guous is that _{a}_{n}=0(x), provided certain fairly mild conditions are satisfied. Copyright.

Original language | English (US) |
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Pages (from-to) | 71-83 |

Number of pages | 13 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*8*(1), 71-83. https://doi.org/10.1080/03610927808827738