Locally integrable function ( $L_{loc}^{1} (U)$ )

A function is locally integrable when its absolute value has finite integral over every compact subset of its domain. It defines a regular distribution by integration against test functions.

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A **locally integrable function** is a function defined on a measurable space (often \(\mathbb{R}^n\) or a subset thereof) that is integrable within every compact subset of its domain.

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