= Locally square-integrable function
{title2=$L^2_{\mathrm{loc}}(U)$}
A measurable <function> belongs to $L^2_{\mathrm{loc}}(U)$ when its squared absolute value has finite integral on every compact subset of $U$. Functions are identified if they agree almost everywhere. This is a local integrability condition, not a specified global <Hilbert space> <norm>. For example, $x$ belongs to $L^2_{\mathrm{loc}}(\mathbb R)$ but its mean-square averages on expanding intervals diverge.
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