L. Korf and R.J-B Wets. Random closed sets and random lsc functions: Kolmogorov's extension theorem. Manuscript, 1998.  Home/Search   Document Not in Database   Summary   Related Articles

.... normal integrand ; see Chapter 14 of [8] for a systematic exposition. The Effros field identifies the oe field of measurable subsets of lsc fcns(X) It s the oe field generated by the sets of the type A D;ff = ff 2 lsc fcns(X) j inf D f ffg; with D either an open or closed subset of X; cf. [3, 5] for more about the properties of the Effros field on lsc fcns(X) To a random lsc function f one associates its distribution P f defined by P f (A) P (f 2 Xi j f( Delta) 2 Ag) for A 2 E : Two random lsc functions, f and g, are identically distributed if for all A 2 E , P f (A) P g ....

....ff ; 2 INg of random lsc functions, let s denote by P 1 the probability measure on the sequence space ( lsc fcns(X) 1 ; E 1 ) that is consistent with the joint distribution of the f . That such a measure exists follows from Kolmogorov s extension theorem for random lsc functions, cf. [5]. Random lsc functions are said to be independent if their distributions are independent. A sequence of random lsc functions ff ; 2 INg of random lsc functions is pairwise independent if for any pair k; l 2 IN and A 1 ; A 2 2 E , P f k ;f l (A 1 ; A 2 ) P f k(A 1 )P f l (A 2 ) The ....

L. Korf and R.J-B Wets. Random closed sets and random lsc functions: Kolmogorov's extension theorem. Manuscript, 1998.

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