The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between diffe

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially

Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation.