Calculus of Variations and Geometric Measure Theory

S. Di Marino - D. Lučić - E. Pasqualetto

Representation theorems for normed modules

created by pasqualetto on 09 Sep 2021



Inserted: 9 sep 2021

Year: 2021

ArXiv: 2109.03509 PDF


In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise representative of their elements; to prove that each separable normed module can be represented as the space of sections of a measurable Banach bundle. By combining our representation result with Gigli's differential structure, we eventually show that every metric measure space (whose Sobolev space is separable) is associated with a cotangent bundle in a canonical way.