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We revisit the classical monotone-follower problem and consider it in ageneralized formulation. Our approach is based on a compactness substitute fornondecreasing processes, the Meyer-Zheng weak convergence, and the maximumprinciple of Pontryagin. It establishes existence under weak conditions,produces general approximation results and further elucidates the celebratedconnection between singular stochastic control and stopping.

Existence, Characterization and Approximation in the Generalized Monotone-Follower Problem