locally integrable function
Definition Suppose that is an open set in , and is a Lebesgue measurable function. If the Lebesgue integral
is finite for all compact subsets in , then is locally integrable. The set of all such functions is denoted by .
Example
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1.
, where is the set of (globally) integrable functions.
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2.
Continuous functions are locally integrable.
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3.
The function for and 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 |