Measure Theory in Noncommutative Spaces

Details Measure Theory in Noncommutative Spaces Measure Theory in Noncommutative Spaces

2010-09-16

arxiv.org/abs/1009.3095v1

SIGMA 6 (2010), 072, 36 pages

Mathematics

Operator Algebras

Scientific paper

10.3842/SIGMA.2010.072

The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.

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