Definition talk:Random Variable

I plan on splitting out Definition 2 into Definition:Real-Valued Random Variable. What should I do with Definition 3? It is a very elementary rewriting of Definition 2, (literally just writing $\set {\omega \in \Omega : \map X \omega \le t} = X^{-1} \sqbrk {\hointl {-\infty} t}$) so elementary that I'm not really sure it justifies its own page. (and is not linked anywhere outside this page and subpages) I ask since deleting content here is frowned upon, but I see no need for def 3. Caliburn (talk) 23:02, 26 December 2021 (UTC)

How about an "Also presented as" section which would hang off the bottom of Definition 1, which would now be the "only" definition (given that Definition 2 is to be a separate thing, a specialised subdefinition)? I have taken to using "Also presented as" when the only thing different is the notation -- although in this case there will need to be a full and frank disclosure of exactly why they are the same thing

But because the notations are completely different, my view is that it is the right way to do 2 separate definitions, with the "equivalence proof" page explaining the above. There are more trivially equivalent definitions than these, and muggles like me who really don't get a lot of the subtleties of measures and probability spaces, we guys need this blow-by-blow explanation of the obviousness of the equivalence, because unless you are in the know, it is far from obvious. --prime mover (talk) 23:11, 26 December 2021 (UTC)