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    A representation theorem for operators on a space of interval functions by J. A. Chatfield

    Published 1978-01-01
    “…In particular we show that TH=(I)∫abfHdα+∑i=1∞[H(xi−1,xi−1+)−H(xi−1+,xi−1+)]β(xi−1)+∑i=1∞[H(xi−,xi)−H(xi−,xi−)]Θ(xi−1,xi)where each of α, β, and Θ depend only on T, α is of bounded variation, β and Θ are 0 except at a countable number of points, fH is a function from R to N depending on H and {xi}i=1∞ denotes the points P in [a,b]. for which [H(p,p+)−H(p+,p+)]≠0 or [H(p−,p)−H(p−,p−)]≠0. …”
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