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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Laws of large numbers without additivity


Author: Pedro Terán
Journal: Trans. Amer. Math. Soc. 366 (2014), 5431-5451
MSC (2010): Primary 60F15; Secondary 28A12, 60A05
Published electronically: June 6, 2014
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Abstract: The law of large numbers is studied under a weakening of the axiomatic properties of a probability measure. Averages do not generally converge to a point, but they are asymptotically confined in a limit set for any random variable satisfying a natural `finite first moment' condition. It is also shown that their behaviour can depart strikingly from the intuitions developed in the additive case.


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Additional Information

Pedro Terán
Affiliation: Departamento de Estadística e I.O. y D.M., Escuela Politécnica de Ingeniería, Universidad de Oviedo, E-33071 Gijón, Spain
Email: teranpedro@uniovi.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06053-4
PII: S 0002-9947(2014)06053-4
Keywords: Capacity, Choquet integral, law of large numbers, non-additive probability
Received by editor(s): July 24, 2012
Received by editor(s) in revised form: December 8, 2012
Published electronically: June 6, 2014
Additional Notes: This paper is dedicated to the memory of Professor Teófilo Brezmes Brezmes, an excellent lecturer and appreciated colleague.
This research was partially funded by Spain’s Ministerio de Ciencia e Innovación (TIN2008-06796-C04-04, MTM2011-22993, ECO1022–24181).
Article copyright: © Copyright 2014 Pedro Ter\'an