Ultrafilter limits provide the natural convergence notion for finitely additive probability. The finitely additive infinitely divisible laws are closed under ultrafilter limits. The characteristic function of any convolution of finitely additive probability measures is the product of their characteristic functions.
First published in Proceedings of the American Mathematical Society 84(4), published by the American Mathematical Society
Sibley TQ. 1982. Ultrafilter limits and finitely additive probability. Proceedings of the American Mathematical Society 84(4): 560–562.