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

Moran, Gadi

doi:10.1090/S0002-9947-1979-0546909-3

Continuous functions on countable compact ordered sets as sums of their increments
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Trans. Amer. Math. Soc. 256 (1979), 99-112 Request permission

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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