This might be a simple question, but it is really confusing. I have not found any explicit definition or example of extended real-valued function.
My guess is that f defined by f: x -> 1/x on (0,1) is REAl-valued, while g defined by g: x -> 1/x on [0,1) is EXTENDED REAL-valued. Is this the case?
Could someone please give some examples?
Best Answer
In general, an $E$-valued function is a function that takes values in $E$.
The extended reals are $\mathbb{R}\cup\{\pm \infty\}$. So an extended-reals-valued function takes values that are either in $\mathbb{R}$, or possibly $\pm \infty$.