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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 6, Fasc. 2,
pages 225 - 232
 

ON SOME CRITERION OF CONVERGENCE IN PROBABILITY

Wiesław Zięba

Abstract: Let (_O_,A,P ) be a probability space. (S,r) denotes a metric space, and B stands for the s -field generated by open sets of S. The set S is assumed to be a separable and complete space. A sequence (X  ,n > 1)
   n of random elements, defined on a probability space (_O_, A,P ) taking values in S, is called stable if for every B  (-  A, with P(B) > 0, there exists a probability measure m
 B  such that

 lim P ([X    (-  A]| B) = m (A).
n--> oo      n          B

There are given conditions concerning the set PA(S) = (mB,B  (-  A) of probability measures, under which there exists a random element X such that the sequence (Xn, n > 1) of random elements converges in probability to X.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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