I would very much appreciate some input on the following.
Assume I have a random variable $v$ on a probability space $(X,F,P)$ and function of the random variable, $f(v)$.Is the statement$$P(\{x\in X \vert f(v(x))< \infty\})=1$$sufficient to claim$$E[f(v)]<\infty$$
If not, what can go wrong? Any hint is higly appreciated.
