  We prove a global fractional differentiability result via the fractional
Caccioppoli-type estimate for solutions to nonlinear elliptic problems with
measure data. This work is in fact inspired by the recent paper [B. Avelin, T.
Kuusi, G. Mingione, {\em Nonlinear Calder\'on-Zygmund theory in the limiting
case}, Arch. Rational. Mech. Anal. {\bf 227}(2018), 663--714], that was devoted
to the local fractional regularity for the solutions to nonlinear elliptic
equations with right-hand side measure, of type $-\mathrm{div}\,
\mathcal{A}(\nabla u) = \mu$ in the limiting case. Being a contribution to
recent results of identifying function classes that solutions to such problems
could be defined, our aim in this work is to establish a global regularity
result in a setting of weighted fractional Sobolev spaces, where the weights
are powers of the distance function to the boundary of the smooth domains.
