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'summable function'
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| Title of object: |
summable function |
| Canonical Name: |
SummableFunction |
| Type: |
Definition |
| Created on: |
2008-07-13 04:43:20 |
| Modified on: |
2008-07-13 04:44:35 |
| Keywords: |
summable integrable Lebesgue |
| Synonyms: |
summable function=integrable function |
Preamble:
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\usepackage{amsmath}
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%\usepackage{psfrag}
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\def\reals{\mathbb{R}} |
Content:
A measurable function $f : \Omega \to \reals$ where $(\Omega, \mathcal{A}, \mu)$ is a measure space is said to be {\bf summable} or {\bf integrable} if the Lebesgue integral of the absolute value of $f$ exists and is finite,
\begin{equation*}
\int_{\Omega} |f| d\mu < +\infty
\end{equation*} |
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