A geometrical approach to monotone functions in R n

This paper is concerned with the fine properties of monotone functions on R. 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 convex function and whose weak Jacobian Ju is supported on a purely unrectifiable set.

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