I'm trying to find a contraction example to show that the space $L^\infty$ is not compactly embedded in $L^1$ with the Lebesgue measure.
Please help me!
2026-03-26 16:10:47.1774541447
Is $L^\infty$ compactly embedded in $L^1$?
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divide the interval [0,1] to N subintervals and take the function $F_N$ as below:
in odd subintervals equal 1
in even subintervals equal 0