Measure, Integration & Real Analysis · Problem 6D.17
L^p Spaces — Sheldon Axler
Mathematics — Measure Theory · hahn-banach-separable-without-axiom-of-choice
Problem
Suppose V is a separable normed vector space. Explain how the Hahn–Banach Theorem (6.69) for V can be proved without using any results (such as Zorn's Lemma) that depend on the Axiom of Choice.
[A normed vector space is called separable if it has a countable subset whose closure equals the whole space.]