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Additional integral inequalities are obtained for integrals of thedifferences of subharmonic functions by Borel measures on balls in amultidimensional Euclidean space. These integrals are still estimated fromabove through the Nevanlinna characteristic and various characteristics of theBorel measure and its support. All the results are also new for logarithms ofmodules of meromorphic functions on discs in the complex plane. Integration byBorel measures with a support on fractal sets is allowed, and estimates inthese cases are given by the Hausdorff measure and the Hausdorff content forthe support of the Borel measure. We consider separately important forapplications special cases of functions in the entire complex plane and space,in the unit disc or ball, as well as cases of integration over length onsubsets of Lipschitz curves and over area on subsets of Lipschitzhypersurfaces.

Integrals of differences of subharmonic functions. III. Hausdorff measure and content, integration over Lipschitz curves and surfaces