We strengthen the well-known Marcinkiewicz–Zygmund law of large numbers in the case of Banach lattices. Examples of applications to empirical distributions are presented.
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J. Marcinkiewicz and A. Zygmund, “Sur les fonctions indépendantes,” Fund. Math., 39, 60–90 (1937).
M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin (1991).
J. Lindenstrauss and L.Tsafriri, Classical Banach Spaces, Springer, Berlin (1979).
I. K. Matsak and A. M. Plichko, “On the law of large numbers in Banach lattices,” Mat. Visn. NTSh, 6, 179–197 (2009).
I. K. Matsak, “A remark on the order law of large numbers,” Teor. Imovir. Mat. Stat., Issue 72, 84–92 (2005).
I. K. Matsak and A. M. Plichko, “On maxima of independent random elements in a functional Banach lattice,” Teor. Imovir. Mat. Stat., Issue 61, 105–116 (1999).
Yu. V. Prokhorov, “On the strengthened law of large numbers,” Izv. Akad. Nauk SSSR, 14, No. 6, 523–536 (1950).
V. V. Petrov, Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).
N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).
V. V. Yurinskii, “Exponential estimates for large deviations,” Teor. Ver. Primen., 19, No. 1, 152–153 (1974).
W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Vol. 2, Mir, Moscow (1984).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 4, pp. 504–513, April, 2010.
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Matsak, I.K., Plichko, A.M. On the Marcinkiewicz–Zygmund law of large numbers in Banach lattices. Ukr Math J 62, 575–587 (2010). https://doi.org/10.1007/s11253-010-0373-z
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DOI: https://doi.org/10.1007/s11253-010-0373-z