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The strong law of large numbers when the mean is undefined. (English) Zbl 0304.60016

##### MSC:
 60F15 Strong limit theorems 60F20 Zero-one laws 60G50 Sums of independent random variables; random walks 60J99 Markov processes
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##### References:
 [1] K. G. Binmore and Melvin Katz, A note on the strong law of large numbers, Bull. Amer. Math. Soc. 74 (1968), 941 – 943. · Zbl 0165.20202 [2] C. Derman and H. Robbins, The strong law of large numbers when the first moment does not exist, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 586 – 587. · Zbl 0064.38202 [3] K. Bruce Erickson, A renewal theorem for distributions on \?\textonesuperior without expectation, Bull. Amer. Math. Soc. 77 (1971), 406 – 410. · Zbl 0217.50504 [4] William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. · Zbl 0077.12201 [5] Harry Kesten, The limit points of a normalized random walk, Ann. Math. Statist. 41 (1970), 1173 – 1205. · Zbl 0233.60062 · doi:10.1214/aoms/1177696894 · doi.org [6] Simon Kochen and Charles Stone, A note on the Borel-Cantelli lemma, Illinois J. Math. 8 (1964), 248 – 251. · Zbl 0139.35401 [7] John A. Williamson, Fluctuations when \?(\?$$_{1}$$)=\infty , Ann. Math. Statist. 41 (1970), 865 – 875. · Zbl 0198.23803 · doi:10.1214/aoms/1177696964 · doi.org
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