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A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refine ment of the Glivenko-Cantelli theorem is obtained, in which a new empiri cal distribution function not only has the usualdoi:10.1214/aop/1176989688 fatcat:5w76sxhvazcgdmj3wvqi4aw7e4