Category:Integral of Integrable Function over Measurable Set
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This category contains results about Integral of Integrable Function over Measurable Set.
Definitions specific to this category can be found in Definitions/Integral of Integrable Function over Measurable Set.
Let $\struct {X, \Sigma, \mu}$ be a measure space, and let $E \in \Sigma$.
Let $f: X \to \overline \R$ be a $\mu$-integrable function.
Then the $\mu$-integral of $f$ over $E$ is defined by:
- $\ds \int_E f \rd \mu := \int \chi_E \cdot f \rd \mu$
where:
- $\chi_E$ is the characteristic function of $E$
- $\chi_E \cdot f$ is the pointwise product of $\chi_E$ and $f$
- the integral sign on the right hand side denotes $\mu$-integration of the function $\chi_E \cdot f$.
Pages in category "Integral of Integrable Function over Measurable Set"
The following 3 pages are in this category, out of 3 total.