Measure theory over boolean toposes
Abstract
In this paper we develop a notion of measure theory over boolean toposes which is analogous to noncommutative measure theory, i.e. to the theory of von Neumann algebras. This is part of a larger project to study relations between topos theory and noncommutative geometry. The main result is a topos theoretic version of the modular time evolution of von Neumann algebra which take the form of a canonical R+*principal bundle over any integrable locally separated boolean topos.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 DOI:
 10.48550/arXiv.1411.1605
 arXiv:
 arXiv:1411.1605
 Bibcode:
 2014arXiv1411.1605H
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Operator Algebras;
 18B25;
 03G30;
 46L10;
 46L51
 EPrint:
 23 pages