Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

``Place functions'': alias continuous functions on the Stone space


Author: I. Fleischer
Journal: Proc. Amer. Math. Soc. 106 (1989), 451-453
MSC: Primary 06E15; Secondary 28A60
MathSciNet review: 967485
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Caratheodory's system of place functions on a Boolean $ \sigma $-ring is shown to be canonically isomorphic--order and algebraically--to the system of continuous extended real-valued functions over its Stone space. This enables one to dispense with the imperspicuous formulae and calculations of [CL] in favor of the more straightforward and familiar ones of function spaces; and to subsume the proposed generalization of integration under standard treatment.


References [Enhancements On Off] (What's this?)

  • [CL] C. Carathéodory, Algebraic theory of measure and integration, Translated from the German by F. E. J. Linton, Chelsea Publishing Co., New York, 1963. MR 0148836 (26 #6340)
  • [S] R. Sikorski, Boolean algebras, 3rd ed. Springer, Berlin, 1969.
  • [V] B. Z. Vulikh, Introduction to the theory of partially ordered spaces, Translated from the Russian by Leo F. Boron, with the editorial collaboration of Adriaan C. Zaanen and Kiyoshi Iséki, Wolters-Noordhoff Scientific Publications, Ltd., Groningen, 1967. MR 0224522 (37 #121)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06E15, 28A60

Retrieve articles in all journals with MSC: 06E15, 28A60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0967485-9
PII: S 0002-9939(1989)0967485-9
Article copyright: © Copyright 1989 American Mathematical Society