locally integrable function

Definition Suppose that U is an open set in n, and f:U is a Lebesgue measurable function. If the Lebesgue integralMathworldPlanetmath


is finite for all compact subsets K in U, then f is locally integrable. The set of all such functions is denoted by Lloc1(U).


  1. 1.

    L1(U)Lloc1(U), where L1(U) is the set of (globally) integrable functions.

  2. 2.

    Continuous functionsMathworldPlanetmathPlanetmath are locally integrable.

  3. 3.

    The function f(x)=1/x for x0 and f(0)=0 is not locally integrable.

Title locally integrable function
Canonical name LocallyIntegrableFunction
Date of creation 2013-03-22 13:44:19
Last modified on 2013-03-22 13:44:19
Owner matte (1858)
Last modified by matte (1858)
Numerical id 11
Author matte (1858)
Entry type Definition
Classification msc 28B15