---- Here, $\mathbb{F}$ denotes $\mathbb{R}$ or $\mathbb{C}$. > [!definition] Definition. ([[locally integrable function]]) > Let $(X, \Sigma, \mu)$ be a [[measure|measure space]], $X \subset \mathbb{R}^{n}$, and let $1 \leq p \leq \infty$. Let $E \in \Sigma$. A [[measurable function|measurable function]] $f: E \to \mathbb{F}$ which belongs [[Lp-norm|to]] $L^{p}(K)$ for any [[compact]] set $K \subset E$ is called a **locally $p$-integrable** function. The [[vector space|space]] of locally integrable functions is denoted $L^{p}_{\text{loc}}(E)$. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```