Abstract
In characterizing the semistable law, [Shimizu reduced the problem to solving the equation\(H(x) = \int_0^\infty {H(x + y)} d(\mu - v)(y)\),x≥0 whereμ andv are given positive measures on [0, ∞). In this note, we obtain a simple proof and show that some of his conditions can be weakened.
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Lau, K., Gu, H. A note on an integrated cauchy functional equation. Acta Mathematicae Applicatae Sinica 5, 105–109 (1989). https://doi.org/10.1007/BF02009743
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DOI: https://doi.org/10.1007/BF02009743