Laws of large numbers without additivity
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- by Pedro Terán PDF
- Trans. Amer. Math. Soc. 366 (2014), 5431-5451
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.References
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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
- 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). - © Copyright 2014 Pedro Terán
- Journal: Trans. Amer. Math. Soc. 366 (2014), 5431-5451
- MSC (2010): Primary 60F15; Secondary 28A12, 60A05
- DOI: https://doi.org/10.1090/S0002-9947-2014-06053-4
- MathSciNet review: 3240929