We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincaré inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.
"Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces." J. Math. Soc. Japan 67 (2) 561 - 579, April, 2015. https://doi.org/10.2969/jmsj/06720561