We identify the possible cluster sets for a general lawof the iterated logarithm in the Banach space setting,and showthat all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable Banach space. This extends previous results obtained in .nite dimensional Euclidean spaces.
"Cluster Sets for a Generalized Law of the Iterated Logarithm in Banch Spaces." Ann. Probab. 29 (4) 1451 - 1475, October 2001. https://doi.org/10.1214/aop/1015345758