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We establish pointwise estimates expressed in terms of a nonlinear potentialof a generalized Wolff type for $A$-superharmonic functions with nonlinearoperator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurabledependence on the spacial variable and Orlicz growth with respect to the lastvariable. The result is sharp as the same potential controls bounds from aboveand from below. Applying it we provide a bunch of precise regularity resultsincluding continuity and H\"older continuity for solutions to problemsinvolving measures that satisfies conditions expressed in the natural scales.Finally, we give a variant of Hedberg--Wolff theorem on characterization of thedual of the Orlicz space.

Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth