``Place functions'': alias continuous functions on the Stone space
Proc. Amer. Math. Soc. 106 (1989), 451-453
Primary 06E15; Secondary 28A60
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Abstract: Caratheodory's system of place functions on a Boolean -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.
Carathéodory, Algebraic theory of measure and
integration, Translated from the German by F. E. J. Linton, Chelsea
Publishing Co., New York, 1963. MR 0148836
R. Sikorski, Boolean algebras, 3rd ed. Springer, Berlin, 1969.
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
- C. Caratheodory, Algebraic theory of measure and integration, Trans., F.E.J. Linton, Chelsea, New York, 1963. MR 0148836 (26:6340)
- R. Sikorski, Boolean algebras, 3rd ed. Springer, Berlin, 1969.
- B.Z. Vulikh, Introduction to the theory of partially ordered spaces, Groningen, 1967. MR 0224522 (37:121)
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