Quote by zli034
There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables.
If you know functions are not random variables please please reply this post.
This class is about set theory, probability measure, Borel sets, sigma algebra, and limsup, liminf of sets.

A random variable is just a measurable function on a measure space of total measure 1.
if the sigma algebra is the Lebesque measurable sets then any continuous function is measurable. E.g. any polynomial. But pretty much any function you can think of is Lebesque measurable. Nonmeasurable functions are difficult to come by.