Many results in probability theory/random matrix theory/etc require probability distributions with finite fourth moments; what is the measure of such probability distributions (in the space of probability measures)?  While the question "what RVs has finite fourth moment" is answered [here][1], I'm trying to determine how often you would expect "real-life data" to conform to hypotheses in the various results above.


  [1]: https://mathoverflow.net/questions/11017/is-there-any-random-variable-which-has-unbounded-fourth-moment "here"