Suppose that f0 is a linear functional defined on a subspace Z of X such that f0(x) ¤ g(x) for every x Z where g

Suppose that f0 is a linear functional defined on a subspace Z of X such that
f0(x) ‰¤ g(x)† for every x ˆˆ Z
where g ˆˆ X* is convex. Show that
1. The sets

and

are convex subsets of the linear space Y = X × „œ (figure 3.21)
2. int A ‰  ˆ… and int Aˆ©B = ˆ….
3. There exists a linear functional

(X), X E