Geodesic
Mapping of sets of finite $\alpha$-measure by rational functions
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 621-633.

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Inequalities are obtained which reflect the changes in the Hausdorff $\alpha$-measures, including lengths and areas, of planar sets when they are mapped by rational functions of a complex variable. Some applications of these inequalities to the theory of rational approximation are given. Bibliography: 13 titles. 
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E. P. Dolzhenko; V. I. Danchenko. Mapping of sets of finite $\alpha$-measure by rational functions. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 621-633. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a8/

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