On existence of rich Fubini extensions

This note presents new results on existence of rich Fubini extensions. The notion of a rich Fubini extension was recently introduced by Sun (J Econ Theory 126:31–69, 2006) and shown by him to provide the proper framework to obtain an exact law of large numbers for a continuum of random variables. In contrast to the existence results for rich Fubini extensions established by Sun, the arguments in this note do not use constructions from nonstandard analysis.