Problem: Show an example of a sequence of measurable positive functions on (0,1) so that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left\|\underline{lim} f_{n}\right\| < \underline{lim}\left\|f_{n}\right\| for n\rightarrow\infty[/tex]

My work: I think its just the indicator function [tex]I_{[n,n+1]}[/tex]

Since [tex]\left\|\underline{lim} I_{[n,n+1]}\right\|= 0 < \underline{lim}\left\|I_{[n,n+1]}\right\| =1 [/tex]

For some reason I do not feel to confident in my answer, so any comments are welcome.

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# Homework Help: Essential supremum

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