@article{1974,
    author = {Tze Leung Lai},
    abstract = {In this paper, we present certain theorems concerning the Cesaro (C, {$\alpha$}), Abel (A), Euler (E, q) and Borel (B) summability of Σ Yi, where Yi = Xi - Xi - 1, X0 = 0 and X1, X2,... are i.i.d. random variables. While the Kolmogorov strong law of large numbers and the Hartman-Wintner law of the iterated logarithm are related to (C, 1) summability and involve the finiteness of, respectively, the first and second moments of X1, their analogues for Euler and Borel summability involve different moment conditions, and the analogues for (C, {$\alpha$}) and Abel summability remain essentially the same.},
    copyright = {Copyright {\copyright} 1974 American Mathematical Society},
    date-added = {2014-02-11 14:03:11 +0000},
    date-modified = {2026-1-15 10:28:34 +0100},
    issn = {00029939},
    journal = {Proceedings of the American Mathematical Society},
    jstor_articletype = {research-article},
    jstor_formatteddate = {Aug., 1974},
    language = {English},
    number = {2},
    pages = {pp. 253-261},
    publisher = {American Mathematical Society},
    title = {{Summability Methods for Independent, Identically Distributed Random Variables}},
    url = {http://www.jstor.org/stable/2040073},
    volume = {45},
    year = {1974},
    bdsk-url-1 = {http://www.jstor.org/stable/2040073},
    file = {Summability Methods for Independent, Identically Distributed Random Variables - Lai (0) (0) - a - a - k.pdf}
}

@article{1974, author = {Tze Leung Lai}, abstract = {In this paper, we present certain theorems concerning the Cesaro (C, {$\alpha$}), Abel (A), Euler (E, q) and Borel (B) summability of Σ Yi, where Yi = Xi - Xi - 1, X0 = 0 and X1, X2,... are i.i.d. random variables. While the Kolmogorov strong law of large numbers and the Hartman-Wintner law of the iterated logarithm are related to (C, 1) summability and involve the finiteness of, respectively, the first and second moments of X1, their analogues for Euler and Borel summability involve different moment conditions, and the analogues for (C, {$\alpha$}) and Abel summability remain essentially the same.}, copyright = {Copyright {\copyright} 1974 American Mathematical Society}, date-added = {2014-02-11 14:03:11 +0000}, date-modified = {2026-1-15 10:28:34 +0100}, issn = {00029939}, journal = {Proceedings of the American Mathematical Society}, jstor_articletype = {research-article}, jstor_formatteddate = {Aug., 1974}, language = {English}, number = {2}, pages = {pp. 253-261}, publisher = {American Mathematical Society}, title = {{Summability Methods for Independent, Identically Distributed Random Variables}}, url = {http://www.jstor.org/stable/2040073}, volume = {45}, year = {1974}, bdsk-url-1 = {http://www.jstor.org/stable/2040073}, file = {Summability Methods for Independent, Identically Distributed Random Variables - Lai (0) (0) - a - a - k.pdf} }