Sobolev-type functions on metric spaces: area and co-area formulas by way of Luzin, Rado, and Reichelderfer

Mathematics – Classical Analysis and ODEs

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Scientific paper

We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit both a Poincar\'e inequality and are equipped with a doubling measure. The properties we have selected to study are those that are closely related to area and coarea formulas. We present these formulas for Newton-Sobolev functions in the abstract metric setting.

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