Abstract
The action and averaging properties of conditional expectation operators are studied in the, measure-free, Riesz space, setting of Kuo, Labuschagne and Watson [Conditional expectations on Riesz spaces. J. Math. Anal. Appl., 303 (2005), 509–521.] but on the abstract L2 space, L2(T) introduced by Labuschagne and Watson [Discrete Stochastic Integration in Riesz Spaces. Positivity, 14, (2010), 859–575.]. In this setting the Bienaymé inequality is proved and from this foundation Bernoulli processes are considered. Bernoulli’s strong law of large numbers and Poisson’s theorem are given.
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© 2016 Springer International Publishing Switzerland
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Kuo, WC., Vardy, J.J., Watson, B.A. (2016). Bernoulli Processes in Riesz Spaces. In: de Jeu, M., de Pagter, B., van Gaans, O., Veraar, M. (eds) Ordered Structures and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27842-1_16
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DOI: https://doi.org/10.1007/978-3-319-27842-1_16
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-27840-7
Online ISBN: 978-3-319-27842-1
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