The Law of the Iterated Logarithm for m-Dependent Banach Space Valued Random Variables

A theorem on the law of the iterated logarithm is established for m-dependent B-valued random variables. The conditions in our theorem match their independent analogues and appear as necessary or minimal for the results. According to an example given in the paper, the situation we face is much different from the finite dimensional case and therefore, so is the way we solve the problems.