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In this paper, we consider a special class of dependent random variables (APND) that contains negative dependent random variables classes(ND,PND,NUOD,NA,NLOD,) and some classes of positive dependent random variables. Then we generalize Kolmogrov–Feller weak law of large numbers for i.i.d. random variables to APND random variables. we further give corresponding forms of dependence for random elements taking values in separable Banach space. This development will be of use for obtaining Banach space weak law of large numbers.

The Kolmogrov–Feller type weak law of large numbers for APND random variables