在数学中，局部可积函数是指在定义域内的所有紧集上都可积的函数。

设为欧几里得空间中的一个开集。设是一个勒贝格可测函数。如果函数在任意紧集上的勒贝格积分都存在：

那幺就称函数为一个-局部可积的函数。所有在上局部可积的函数的集合一般记为：

可测

其中指包含的所有的紧集的集合。

一般测度空间

对于更一般的测度空间，也可以类似地定义其上的局部可积函数。

In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition. The importance of such functions lies in the fact that their function space is similar to L_p spaces, but its members are not required to satisfy any growth restriction on their behavior at infinity: in other words, locally integrable functions can grow arbitrarily fast at infinity, but are still manageable in a way similar to ordinary integrable functions.