Are continuous functions of random variables, random variables too?
For example, , for being a random variable. Is it a r.v?
A random variable is a measurable application (from a space to another).
A continuous function is measurable *provided you are in a correct sigma-algebra, as Laurent pointed out below ^^.
The composition of two measurable functions is measurable.
Thus the composition of a continuous function and a random variable is a random variable