Abstract
In this exposition we investigate almost sure convergence for weighted U-statistics. This strong law of large numbers is established for a class of divergent series of non-negative weights when the product of the kernel of the underlying weighted U-statistics and its logarithm is integrable. This result is used to establish the almost sure validity of incomplete U-statistics. Also, a method of constructing incomplete U-statistics of order 2 is introduced and its almost sure validity is established.
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