Abstract
We parametrize continuous self-affine functions defined in [3] and represent them by the infinite sum. We also give a necessary and sufficient condition so that a self-affine function has absolutely continuous distribution with respect to the Lebesgue measure. Moreover we discuss surface filling functions defined by two self-affine functions and compare these with those constructed by D. Hilbert [4].
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Editor’s Note Two articles in this issue, “Sur la Mesure d’Occupation d’une Classe de Fonctions Self-Affines” by Jean Bertoin, and “On Self-Affine Functions” by Norio Kôno, containing essentially the same results, were submitted to our editorial office almost at the same time. We believe that these works were achieved independently.
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Kôno, N. On self-affine functions II. Japan J. Appl. Math. 5, 441–454 (1988). https://doi.org/10.1007/BF03167911
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DOI: https://doi.org/10.1007/BF03167911