Weakly compactly generated Banach spaces and the strong law of large numbers (Q1314311)

The author studies the structure of a random variable, taking values in a Banach space, such that independent copies of the random variable satisfy the strong law of large numbers. If the Banach space coincides with the closed linear span of a compact in the weak topology, then the random variable can be represented as sum of a random variable with finite Bochner mean and a random variable with zero Pettis norm (i.e., the expectation of any linear continuous functional of this random variable equals zero). The decomposition is unique.