Frontmatter -- Contents -- New stability results for sequences of metric measure spaces with uniform Ricci bounds from below -- Surface 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 ∞-Poincarâe inequality and existence ∞-harmonic functions -- Scalar Curvature and Intrinsic Flat Convergence

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. List of contributors: Luigi Ambrosio, Vladimir I. Bogachev, Fabio Cavalletti, Guido De Philippis, Shouhei Honda, Tom Leinster, Christian Lâeonard, Andrea Marchese, Mark W. Meckes, Filip Rindler, Nageswari Shanmugalingam, Takashi Shioya, and Christina Sormani.

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 21. Aug 2017).

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