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It is well known that whenever $p\in (0,1)$, the mapping $$ d_p(x,y):=\|x-y\|_{\ell^p}:=\left(\sum_{n=1}^\infty |x_n-y_n|^p\right)^\frac{1}{p} $$ turns $$\ell^p:=\{(x_n)_{n\in \mathbb N}:\|x\|_{\ell^p}<\infty\}$$ into a complete metric space.

Are there interesting applications of these spaces? I'm aware of the somewhat related Hamming distance, but I am wondering whether something more substantially mathematical exists.

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