Interesting that you say that. I've skimmed but have been meaning to properly read Nelson's: Radically Elementary probability theory http://www.math.princeton.edu/~nelson/books/rept.pdf and http://www.stat.umn.edu/geyer/nsa/. They do away with that problem all together as well as infinite constructions (replaced by hyperfinite) by replacing measure theory with non standard analysis. The gain is at least increased intuitiveness.