Gigli N. Measure Theory in Non-Smooth Spaces

De Gruyter, 2017. — 346 p. — (Partial Differential Equations and Measure Theory). — ISBN 13 9783110550825.Analysis in singular spaces is becoming an increasingly important area of research, with motivation coming from the calculus of variations, PDEs, geometric analysis, metric geometry and probability theory, just to mention a few areas. In all these fields, the role of measure theory is crucial and an appropriate understanding of the interaction between the relevant measure-theoretic framework and the objects under investigation is important to a successful research.
The aim of this book, which gathers contributions from leading specialists with different backgrounds, is that of creating a collection of various aspects of measure theory occurring in recent research with the hope of increasing interactions between different fields.New stability results for sequences of metric measure spaces with uniform Ricci
bounds from belowSurface measures in infinite-dimensional spaces
An Overview of L1 optimal transportation on metric measure spaces
On a conjecture of Cheeger
The magnitude of a metric space: from category theory to geometric measure theory
On the convexity of the entropy along entropic interpolations
Brief survey on1-Poincaré inequality and existence of1-harmonic functions
Metric measure limits of spheres and complex projective spaces
Scalar Curvature and Intrinsic Flat Convergence