Can someone give me an example of an $L ^1$ function which does not belong to $L^\infty$. In fact we look at $L^1(\Omega,\mathcal{F},P)$, where $(\Omega,\mathcal{F},P)$ denotes a probability space. Of course the function should be unbounded but the integral should exist. Clearly, we can embed $L^\infty$ into $L^1$ in this case. Thank you.
A function which is in $L^1$ but does not belong to $L^\infty$
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real-analysis
measure-theory
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1On what measure space? – 2012-10-01