where U2 = G( + 0) G(i0) > 0. Comprehensive developments of the theory of infinitely divisible distributions are contained in books by Gnedenko and Kolmogorov [4], Loeve [7], and Lukacs [8]. It is easy to see that M is absolutely continuous over (oo, 0) u (0, oo) if and only if Gis, and the same statement can be made for the properties: continuous singular and discrete. A problem that has been considered for some time in connection with infinitely divisible distributions is that of their Lebesgue properties
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Howard G. Tucker (1965) studied this question.