  Additional integral inequalities are obtained for integrals of the
differences of subharmonic functions by Borel measures on balls in a
multidimensional Euclidean space. These integrals are still estimated from
above through the Nevanlinna characteristic and various characteristics of the
Borel measure and its support. All the results are also new for logarithms of
modules of meromorphic functions on discs in the complex plane. Integration by
Borel measures with a support on fractal sets is allowed, and estimates in
these cases are given by the Hausdorff measure and the Hausdorff content for
the support of the Borel measure. We consider separately important for
applications 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 on
subsets of Lipschitz curves and over area on subsets of Lipschitz
hypersurfaces.
