Is it true that all differentiable square-integrable functions tend to zero at $\pm \infty$? If that is not true could you give a counterexample?
2026-03-31 05:08:20.1774933700
Square-integrable functions tend to zero at $\pm \infty$
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Let $f =\sum\limits_{n=1}^{\infty} nI_{(n,n+\frac 1 {n^{4}})}$. Can you see that this is a counterexample?