I cannot find the definition of this symbol $L^1_{loc}(U)$ in this book (If the link doesn't start to download, copy it nad paste into your browser.) in the definition above (3).
2026-03-26 22:51:53.1774565513
what does it mean: $L^1_{loc}(U)$
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It means that the function is locally $L^1$, i.e. it is in $L^1(K)$ for every compact subset $K$ of $U$.