It must be admitted that this is the most profound question I have ever seen in the forum. I don't want to answer simply: mathematical expectation is absolutely integrable when defined, and it needs to be verified and judged in theory. At that time, when it was time to define mathematical expectation, there were indeed many mathematicians who directly defined it as integral (regardless of absolute convergence). However, with the deepening of the research on the convergence of random variable value domain, some strange examples have been found. . . . [ ]