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 . 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, is locally integrable on , as is any continuous function.

# Locally Integrable

## See also

Frechet Space, Integrable, Lebesgue Integrable, L1-Space
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Locally Integrable." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/LocallyIntegrable.html