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Proceedings of the American Mathematical Society

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``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
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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
  • [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

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Article copyright: © Copyright 1989 American Mathematical Society