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
modified by lučić on 26 Jun 2020


Published Paper

Inserted: 8 mar 2018
Last Updated: 26 jun 2020

Journal: Rendiconti del Circolo Matematico di Palermo
Pages: 20
Year: 2018
Doi: 10.1007/s12215-018-0366-6

ArXiv: 1803.02911 PDF


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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