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Proyecciones (Antofagasta) - REGULAR CONDITIONAL PROBABILITY, DISINTEGRATION OF PROBABILITY AND RADON SPACES

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.23 n.1 Antofagasta mayo 2004

http://dx.doi.org/10.4067/S0716-09172004000100002 

Proyecciones
Vol. 23, No 1, pp. 1-13, May 2004.
Universidad Católica del Norte
Antofagasta - Chile

REGULAR CONDITIONAL PROBABILITY,
DISINTEGRATION OF PROBABILITY AND
RADON SPACES

D. LEAO Jr. a, M. FRAGOSO b* and P. RUFFINO †c

a Universidade de Sao Paulo, Brasil
b LNCC, Brasil
c Universidad Estadual de Campinas, Brasil

Received : September 2002. Accepted : November 2003.

 

Abstract

We establish equivalence of several regular conditional probability properties and Radon space. In addition, we introduce the universally measurable disintegration concept and prove an existence result.

Keywords : regular conditional probability, Radon space, separable Hausdor, Hausdorff measurable space, disintegration of probability.

AMS classification: 60A10, (93E20).

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*Research supported, in part, by CNPq under grants N 520367/97-9 and N 36.5532/2000-4, and PRONEX.

††Written during a Sabbatical visit to theMathematical Institute, University of Oxford, UK. Research supported by FAPESP grant No. 00/04591-3.

D. Leao Jr.
Departamento de Ciência da Computaçao e Estatística
ICMC - USP
Brasil
e-mail : leao@icmc.sc.usp.br

Marcelo D. Fragoso
LNCC
Petrópolis
Río de Janeiro
Brasil

and

R. C. Ruffino
Departamento de Matemática
Universidade Estadual de Campinas
13081-970 - Campinas - SP
Brasil
e-mail : ruffino@ime.unicampo.br