In 1946 Feller proposed and proved a famous law of iterated logarithm. Unfortunately his proofs were found to be incorrect, although the main result was true. In this paper the author gives a new proof of the main result.
Z. D. Bai. "A Theorem of Feller Revisited." Ann. Probab. 17 (1) 385 - 395, January, 1989. https://doi.org/10.1214/aop/1176991518