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January 2004 Convergence in distribution of nonmeasurable random elements
Patrizia Berti, Pietro Rigo
Ann. Probab. 32(1A): 365-379 (January 2004). DOI: 10.1214/aop/1078415839


A notion of convergence in distribution for non (necessarily) measurable random elements, due to Hoffmann-Jørgensen, is characterized in terms of weak convergence of finitely additive probability measures. A similar characterization is given for a strengthened version of such a notion. Further, it is shown that the empirical process for an exchangeable sequence can fail to converge, due to the nonexistence of any measurable limit, although it converges for an i.i.d. sequence. Because of phenomena of this type, Hoffmann-Jørgensen's definition is extended to the case of a nonmeasurable limit. In the extended definition, naturally suggested by the main results, the limit is a finitely additive probability measure.


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Patrizia Berti. Pietro Rigo. "Convergence in distribution of nonmeasurable random elements." Ann. Probab. 32 (1A) 365 - 379, January 2004.


Published: January 2004
First available in Project Euclid: 4 March 2004

zbMATH: 1049.60004
MathSciNet: MR2040786
Digital Object Identifier: 10.1214/aop/1078415839

Primary: 60A05 , 60B10

Keywords: Convergence in distribution , empirical process , exchangeability , Extension‎ , finitely additive probability measure , measurability

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1A • January 2004
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