Abstract
A bounded law of the iterated logarithm for martingales with values in a separable Hilbert space H is proved. It is then applied to prove invariance principles for U-statistics for independent identically distributed (ℝ-valued) random variables {Xj, j≧1} and a kernel h: ℝm→H, m≧2, which is degenerate for the common distribution function of Xj, j≧1. This extends to general m results of an earlier paper on this subject and even gives new results in the case H=ℝ.
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