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A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactorydoi:10.4236/jamp.2016.41019 fatcat:gscb5v7lmvgdjlaq6tcsmypng4