Accession Number:

AD0653071

Title:

REDUCED POWERS OF THE REAL NUMBER SYSTEM AND EQUIVALENTS OF THE HAHN-BANACH EXTENSION THEOREM.

Descriptive Note:

Technical rept.,

Corporate Author:

CALIFORNIA INST OF TECH PASADENA DEPT OF MATHEMATICS

Personal Author(s):

• Luxemburg,W. A. J.

Report Date:

1967-04-01

Pagination or Media Count:

32.0

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.

Descriptors:

• *FUNCTIONAL ANALYSIS
• *REAL NUMBERS
• *ALGEBRA
• THEOREMS
• SET THEORY
• MAPPING(TRANSFORMATIONS)
• RINGS(MATHEMATICS)
• TOPOLOGY
• BANACH SPACE
• MODEL THEORY
• CONVEX SETS
• SEQUENCES(MATHEMATICS)

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE