Reduced Powers of the Real Number System and Equivalents of the Hahn-Banach Extension Theorem
Abstract
One of the main principles of functional analysis is the so-called Hahn-Banach extension theorem. In the present paper we are mainly interested in the question which other statements in mathematics can be shown to be effectively equivalent to the Hahn-Banach extension theorem. The main result can be phrased as follows: The Hahn-Banach extension theorem is effectively equivalent to the statement every non-degenerate Boolean algebra admits a non-trivial measure. The method being used is to consider the linear ring of finite elements in a reduced power of the real number system. It is shown that this linear ring is an abstract M-space in the sense of Kakutani. Some of the consequences of this fact are given in the present paper.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1967
- Accession Number
- AD0653071
Entities
People
- W. A. Luxemburg
Organizations
- California Institute of Technology