Definition
Given a real vector space {% X %} and a subspace of {% X %}, {% U %}, and a linear map {% \phi(x) %} such that
{% \phi(x) \leq p(x) %}
for {% x %} in {% U %} and for a
sublinear map
{% p(x) %}
, thre exists a
linear map
{% f: X \rightarrow \mathbb{R} %}
such that
{% f(x) = \phi(x) %}
for {% x\in U %}, and
{% f(x) \leq p(x) %}
for {% x \in X %}.
If {% p %} is a seminorm, then
{% |f(x)| \leq p(x) %}
for {% x \in X %}.