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We obtain the analogue of the classical result by Erd\"os and Kac on thelimiting distribution of the maximum of partial sums for exchangeable randomvariables with zero mean and variance one. We show that, if the conditions ofthe central limit theorem of Blum et al. hold, the limit coincides with theclassical one. Under more general assumptions, the probability of the randomvariables having conditional negative drift appears in the limitingdistribution.

The limit theorem for maximum of partial sums of exchangeable random variables