Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces

Abstract

Abstract We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of $${\textrm{RCD}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>RCD</mml:mtext></mml:math> spaces. In the infinite dimensional setting, we are able to define an analogue of the distributional differential and, on finite dimensional spaces, we prove fine properties and suitable calculus rules, such as the Vol’pert chain rule for vector valued functions.