Category:Locally Integrable Functions

This category contains results about Locally Integrable Functions.

Let $f : \R^d \to \C$ be a function.

Let $K \subseteq \R^d$ be a compact subset.

Suppose:

$\ds \forall K \subseteq \R^d : \int_K \size {\map f {\mathbf x} } \rd {\mathbf x} < \infty$

where $\mathbf x \in \R^d$ and $\rd {\mathbf x}$ and $\rd {\mathbf x} = \rd x_1 \rd x_2 \ldots \rd x_d$ is the volume element in $\R^d$.

This article, or a section of it, needs explaining. In particular: Clarify the above, the "and $\rd {\mathbf x}$ and $\rd {\mathbf x}$" is confusing and ambiguous You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

Then $f$ is called the locally integrable function.