Definition:Support
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The support of a mapping can have different meanings depending on the properties of the mapping under consideration.
Definition
Real-Valued Function on an Abstract Set
Let $f: S \to \R$ be a real-valued function.
The support of $f$ is the set of elements $x$ of $S$ whose values under $f$ are non-zero.
That is:
- $\operatorname{supp} \left({f}\right) = \left\{{x \in S: f \left({x}\right) \ne 0}\right\}$
Continuous Real-Valued Function in $\R^n$
Let $f: \R^n \to \R$ be a continuous real-valued function.
The support of $f$ is the closure of the set of elements $x$ of $\R^n$ whose values under $f$ are non-zero.
That is:
- $\operatorname{supp} \left({f}\right) = \overline{\left\{{x \in \R^n: f \left({x}\right) \ne 0}\right\}}$
General Real-Valued Function in $\R^n$
Distribution
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