:: Only statement (2) makes an assumption of finite expectations. A and B are random variables, the terminology implies they are real-valued. Every single TEP variant is about monetary values or utility, always supposed to be real valued. My longer paper shows how the mathematical facts mentioned here deal with every knoen TEP variant, including the other exchange paradoxes (neckties, cards). Statement (4) can be used to deal with the infinite expectation variants of TEP. The utility of money is a strictly monotone, bounded, function of the actual amount. Statement (4) implies that it is impossible that E(B|A=a) > a for all a, where A and B are the utilites of the amounts of money in the two envelopes, not the amounts themselves. So, iNic, this little bit of mathematics is useful for anyone who studies TEP and understands elementary probability theory. But for those who want to study TEP but can't appreciate elementary probability theory, it is difficult to say anything useful at all, I'm sorry about that.