The strong law of large numbers when the mean is undefined

Author:
K. Bruce Erickson

Journal:
Trans. Amer. Math. Soc. **185** (1973), 371-381

MSC:
Primary 60G50; Secondary 60F15

DOI:
https://doi.org/10.1090/S0002-9947-1973-0336806-5

MathSciNet review:
0336806

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Abstract | References | Similar Articles | Additional Information

Abstract: Let where are i.i.d. random variables with . An integral test is given for each of the three possible alternatives a.s.; a.s.; and a.s. Some applications are noted.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0336806-5

Keywords:
Independent identically distributed random variables,
mean undefined,
strong law of large numbers,
renewal function,
truncated mean function

Article copyright:
© Copyright 1973
American Mathematical Society