Abstract
In this theorem the ak and bk are real and the nk are positive but not necessarily integral. The latter point is important for applications. The Law of the Iterated Logarithm for lacunary series has already been treated in the literature. In the first place, Salem and Zygmund [I ] (numbers in square brackets refer to the bibliography at the end of the paper) have shown that under the hypotheses (1.2) we have (1.3) with ? instead of . They also presuppose that the nk are integers. A complete proof of (1.3) was given later by Erdos and Gal [I] under the restriction however
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