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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Continuous functions on countable compact ordered sets as sums of their increments


Author: Gadi Moran
Journal: Trans. Amer. Math. Soc. 256 (1979), 99-112
MSC: Primary 46E15; Secondary 40A30, 54C05
MathSciNet review: 546909
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Abstract: Every continuous function from a countable compact linearly ordered set A into a Banach space V (vanishing at the least element of A ) admits a representation as a sum of a series of its increments (in the topology of uniform convergence). This series converges to no other sum under rearrangements of its terms. A uniqueness result to the problem of representation of a regulated real function on the unit interval as a sum of a continuous and a steplike function is derived.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0546909-3
Keywords: Countable compact ordered set, continuous function, increments, regulated function
Article copyright: © Copyright 1979 American Mathematical Society