Geodesic
Smooth measures and the law of the iterated logarithm
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 455-463

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A measure $\mu$ defined on the unit circle $\partial\mathbf D$ is called smooth if $|\mu(I')-\mu(I'')|\leqslant C|I'|$ for any two adjacent intervals, $I',I''\subset\partial\mathbf D$ of equal length. It is shown that smooth measures are absolutely continuous with respect to Hausdorff measure with weight function $t(\log\frac1t\log\log\log\frac1t)^{1/2}$, and that this result is sharp. The results are applied to the well-known problem of the angular derivative of a univalent function. Bibliography: 14 titles. 
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     author = {N. G. Makarov},
     title = {Smooth measures and the law of the iterated logarithm},
     journal = {Izvestiya. Mathematics },
     pages = {455--463},
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     volume = {34},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a12/}
}
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N. G. Makarov. Smooth measures and the law of the iterated logarithm. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 455-463. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a12/