Category:Sublinear Functionals

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This category contains results about Sublinear Functionals.
Definitions specific to this category can be found in Definitions/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:      \(\ds \forall x \in E, \forall \lambda \in \R_{>0}:\)    \(\ds \map p {\lambda x} \)   \(\ds = \)   \(\ds \lambda \map p x \)      

Subcategories

This category has only the following subcategory.