Category:Integrable Functions (Measure Space)
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This category contains results about Integrable Functions (Measure Space) in the context of Measure Spaces.
Definitions specific to this category can be found in Definitions/Integrable Functions (Measure Space).
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $f \in \MM_{\overline \R}, f: X \to \overline \R$ be a measurable function.
Then $f$ is said to be $\mu$-integrable if and only if:
- $\ds \int f^+ \rd \mu < +\infty$
and
- $\ds \int f^- \rd \mu < +\infty$
where $f^+$, $f^-$ are the positive and negative parts of $f$, respectively.
The integral signs denote $\mu$-integration of positive measurable functions.
Subcategories
This category has only the following subcategory.
I
Pages in category "Integrable Functions (Measure Space)"
The following 5 pages are in this category, out of 5 total.