Locally Integrable

A function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. The space of locally integrable functions is denoted L_(loc)^1. Any integrable function is also locally integrable. One possibility for a nonintegrable function which is locally integrable is if it does not decay at infinity. For instance, f(x)=1 is locally integrable on R, as is any continuous function.

See also

Frechet Space, Integrable, Lebesgue Integrable, L1-Space

This entry contributed by Todd Rowland

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Rowland, Todd. "Locally Integrable." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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