Can anyone come up with an example of a function $f$ which is Lebesgue integrable on $[0,1]$, but max{$f,0$} is NOT Lebesgue integrable? Thanks.
2026-03-31 13:26:21.1774963581
Example of a function $f$ which is Lebesgue integrable on $[0,1]$, but max{$f,0$} is NOT Lebesgue integrable?
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By definition $f$ is Lebesgue integrable if and only if the functions $f_+ =\max\{ f ,0\}$ and $f_- =\max\{-f ,0\}$ are integrable.