Category:Definitions/Sublinear Functionals
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This category contains definitions related to Sublinear Functionals.
Related results can be found in Category:Sublinear Functionals.
Let $E$ be a vector space over $\R$.
A real-valued function $p: E \to \R$ is called a sublinear functional if and only if it satisfies:
\((1)\) | $:$ | Subadditivity: | \(\ds \forall x, y \in E:\) | \(\ds \map p {x + y} \) | \(\ds \le \) | \(\ds \map p x + \map p y \) | |||
\((2)\) | $:$ | Positive Homogeneity: | \(\ds \forall x \in E, \forall \lambda \in \R_{>0}:\) | \(\ds \map p {\lambda x} \) | \(\ds = \) | \(\ds \lambda \map p x \) |
Pages in category "Definitions/Sublinear Functionals"
The following 2 pages are in this category, out of 2 total.