Statement:
The Hahn-Banach Theorem for Separable Normed Linear Spaces: Assume \(V\) is a separable normed linear space and \(p :V \to \Bbb R\) satisfies \(p(x+y) \le p(x) + p(y)\) and \((\forall t \ge 0)(\forall x \in V)(p(tx) = tp(x))\) and assume \(f\) is a linear function from a subspace \(S\) of \(V\) into \(\Bbb R\) which satisfies \((\forall x \in S)(f(x) \le p(x))\), then \(f\) can be extended to \(f^* :V \to \Bbb R\) so that \(f^* \) is linear and \((\forall x \in V)(f^*(x) \le p(x))\).
Howard_Rubin_Number: 287
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Book references
Note connections:
Note 145
A proof that Form 287 (the Hahn-Banach theorem for separable normed linear spaces) implies Form 222 (there is a non-principal measure on \(\omega\)).