A new proof of Kelley's Theorem

S. Ng

Fundamenta Mathematicae (1991)

  • Volume: 140, Issue: 1, page 63-67
  • ISSN: 0016-2736

Abstract

top
Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

How to cite

top

Ng, S.. "A new proof of Kelley's Theorem." Fundamenta Mathematicae 140.1 (1991): 63-67. <http://eudml.org/doc/211929>.

@article{Ng1991,
abstract = {Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.},
author = {Ng, S.},
journal = {Fundamenta Mathematicae},
keywords = {Boolean algebra; measure algebra; Kelley's theorem},
language = {eng},
number = {1},
pages = {63-67},
title = {A new proof of Kelley's Theorem},
url = {http://eudml.org/doc/211929},
volume = {140},
year = {1991},
}

TY - JOUR
AU - Ng, S.
TI - A new proof of Kelley's Theorem
JO - Fundamenta Mathematicae
PY - 1991
VL - 140
IS - 1
SP - 63
EP - 67
AB - Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.
LA - eng
KW - Boolean algebra; measure algebra; Kelley's theorem
UR - http://eudml.org/doc/211929
ER -

References

top
  1. [F] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebra, Vol. III, J. D. Monk and R. Bonnet (eds.), North-Holland, Amsterdam 1989, 877-980. 
  2. [HL] A. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, New York 1985. Zbl0583.26006
  3. [K] J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177. Zbl0087.04801
  4. [L] T. L. Lindstrøm, An invitation to nonstandard analysis, in: Nonstandard Analysis and its Applications, N.J. Cutland (ed.), Cambridge University Press, 1988, 1-105. Zbl0658.03044

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.