Summary
Recently R. C. Powers characterized the order automorphisms of the space of nondecreasing functions from one compact real interval to another [6, 7]. In this paper we show how his results, as well as the lattice-theoretic techniques which he employed, can be used to obtain solutions of Cauchy's equation for certain classes of semigroups (triangle functions) on the space Δ+ of probability distribution functions of nonnegative random variables.
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Riedel, T. Cauchy's equation on Δ+ . Aeq. Math. 41, 192–211 (1991). https://doi.org/10.1007/BF02227455
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DOI: https://doi.org/10.1007/BF02227455