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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

  • 1
    What's the variable $c$?2012-03-02
  • 2
    There's obviously a typo there, since $c$ is never mentioned and appears *ex nihilo* on the right hand side.2012-03-02

1 Answers 1