I can't make sense of the following definition of supremum of sequence of functions.
This definition comes from Garden of Integrals (Burk), chapter 5 (page 99): $$\sup\left\{f_{k}(x),f_{k+1}(x),\ldots \right \}=\bigcup_{n\geq k}\left \{ x \in E: f_{n}(x)>c \right\}$$ where all $f$'s are defined on $E$. How can supremum over $f$'s can yield a union of sets taking values from $E$?
Thanks