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Created: 2025/04/07 09:13
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| Term                    | Description                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| ----------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| Absolutely convergent   | An infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ${\displaystyle \textstyle \sum _{n=0}^{\infty }a_{n}}\textstyle\sum_{n=0}^\infty a_n$ is said to converge absolutely if ${\displaystyle \textstyle \sum _{n=0}^{\infty }\left\|a_{n}\right\|=L}\textstyle\sum_{n=0}^\infty \left\|a_n\right\| = L$ for some real number ${\displaystyle \textstyle L.}$ |
| Absolutely intregreable | A [function](https://en.wikipedia.org/wiki/Function_\(mathematics\) "Function (mathematics)") whose [absolute value](https://en.wikipedia.org/wiki/Absolute_value "Absolute value") is [integrable](https://en.wikipedia.org/wiki/Lebesgue_integration "Lebesgue integration"), meaning that the integral of the absolute value over the whole [domain](https://en.wikipedia.org/wiki/Domain_of_a_function "Domain of a function") is finite.                                                                |