The greatest lower bound is found in the law of the iterated logarithm for the maximum scheme.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 8, pp. 1132–1137, August, 2012.
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Akbash, K.S., Matsak, I.K. One improvement of the law of the iterated logarithm for the maximum scheme. Ukr Math J 64, 1290–1296 (2013). https://doi.org/10.1007/s11253-013-0716-7
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DOI: https://doi.org/10.1007/s11253-013-0716-7