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The purpose of this paper is to present some results related to the dispersive ordering of probability distributions via dispersion functions of the ℒ1-random variables. A new approach to the Laws of Large Numbers in ℒ1-norm can be applied via received results. A new concept on minimum-dispersive unbiased estimator is considered, too.doi:10.1155/2013/780587 fatcat:bmyojfz2h5b3fekf7xwngadjmi