Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 134, Issue 9, Pages 2739-2744Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-06-08296-7
Keywords
weighted averages; limit theorems; pairwise independence
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We show that for a large class of positive weights including the ones that are eventually monotone decreasing and those that are eventually monotone increasing but vary regularly, if the averages of random variables converge in some sense, then their corresponding weighted averages also converge in the same sense. We will also replace the sufficient conditions in the fundamental result of Jamison, Pruitt, and Orey for i.i.d. random variables that make their work more transparent.
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