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Acknowledgment of Priority
Chen, X.: The limit law of the iterated logarithm. J. Theor. Probab.
Xia Chen 0
0 Department of Mathematics, University of Tennessee , Knoxville, TN , USA
Professor Uwe Einmahl brought the following fact to my attention: The limit law established in Theorem 1.1 of  was obtained by Robbins and Siegmund , in the context of Brownian motions rather than random walk. Actually, the result of Robbins and Siegmund provides an asymptotic order that is higher than the one described in Theorem 1.1 of . As also pointed out by Professor Einmahl, the work of Robbins and Siegmund appears (to some degree) as a response to conjectures made by Darling and Erdös .