Calculus of Variations and Geometric Measure Theory
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D. Lučić - E. Pasqualetto

The Serre-Swan theorem for normed modules

created by pasqualetto on 08 Mar 2018



Inserted: 8 mar 2018
Last Updated: 8 mar 2018

Pages: 26
Year: 2018


The aim of this note is to analyse the structure of the $L^0$-normed $L^0$-modules over a metric measure space. These are a tool that has been introduced by N. Gigli to develop a differential calculus on spaces verifying the Riemannian Curvature Dimension condition. More precisely, we discuss under which conditions an $L^0$-normed $L^0$-module can be viewed as the space of sections of a suitable measurable Banach bundle and in which sense such correspondence can be actually made into an equivalence of categories.


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