How can I calculate $\infty-$ norm of this quantity in measure theory$\| \sum_{k=n + 1}^{\infty} \chi_{E_{k}}||_{\infty}$?
where $E_{k}'s$ are disjoint and knowing that $$\lim_{n\rightarrow \infty} \sum_{k= n+1}^{\infty} \mu(E_{k}) = 0 \quad(1)$$
2026-04-09 07:45:10.1775720710
How can I calculate $\infty-$ norm of this quantity in measure theory.?
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$\|\sum\limits_{k=n+1}^{\infty}\chi_{E_k}\|_{\infty}=1$ if $\mu (E_k) >0$ for some $k >n$ and $0$ otherwise.