The paper is concerned with the fine properties of monotone functions on R~n. We study the continuity and differentiability properties of these functions, the approximability properties, the structure of the distributional derivatives and of the weak Jacobians. Moreover, we exhibit an example of a monotone function u which is the gradient of a C~(1, #alpha#) convex function and whose weak Jacobian Ju is supported on a purely unrectifiable set.
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