Abstract :
In their 1993 paper, W. Goh and J. Wimp derive interesting asymptotics for the moments cn(α) ≡ cn = ∫10tndα(t), n = 0, 1, 2, ..., of some singular distributions α (with support ⊂ [0, 1]), which contain oscillatory terms. They suspect, that this is a general feature of singular distributions and that this behavior provides a striking contrast with what happens for absolutely continuous distributions. In the present note, however, we give an example of an absolutely continuous measure with asymptotics of moments containing oscillatory terms, and an example of a singular measure having very regular asymptotic behavior of its moments. Finally, we give a short proof of the fact that the drop-off rate of the moments is exactly the local measure dimension about 1 (if it exists).
