Riemann -summability of independent, identically distributed random variables

Author:
Jack Cuzick

Journal:
Proc. Amer. Math. Soc. **83** (1981), 119-124

MSC:
Primary 40G99; Secondary 60G50

DOI:
https://doi.org/10.1090/S0002-9939-1981-0619995-4

MathSciNet review:
619995

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be i.i.d. random variables. It is shown that is a sufficient condition for Riemann -summability of to . Counterexamples are provided which indicate that the strongest possible necessary condition of moment type is . However under weak regularity conditions on the tails of the distribution of the sufficient condition is also shown to be necessary.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0619995-4

Keywords:
Riemann summability,
random Fourier series,
almost sure convergence

Article copyright:
© Copyright 1981
American Mathematical Society