Vol. 20, No. 1, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
A theorem on lattice ordered groups, results of Ptak, Namioka and Banach, and a front-ended proof of Lebesgue’s theorem

Stephen Simons

Vol. 20 (1967), No. 1, 149–153

The main theorem in this paper is on (not necessarily commutative) lattice ordered groups, and is a generalization of a result on finitely additive set functions due to Namioka. Our result can be used to prove Ptak’s combinatorial theorem on convex means, to give a short non measure-theoretic proof of Lebesgue’s dominated convergence theorem for a sequence of continuous functions on a countably compact topological space, and to give a short proof of Banach’s criteria for the weak convergence of a sequence in the Banach space of all bounded, real functions on an abstract set.

Mathematical Subject Classification
Primary: 46.06
Received: 19 November 1965
Published: 1 January 1967
Stephen Simons