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This article consists of two parts. The first ( § §2-5) is devoted to some questions of analysis in the space of functions whose generalized derivatives are measures (the spaces BV). The results obtained here are applied in the second part ( § §6-7) to the study of quasilinear equations. In §6 we prove a theorem on the existence in the large and the uniqueness of the solution of the Cauchy problem for a first-order quasilinear equation. In §7 we consider quasilinear operators in nondivergence form acting on discontinuous functions in BV.

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