Equivariant measurable liftings
Functional Analysis
2014-05-19 v2 Dynamical Systems
Group Theory
Abstract
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semi-simple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to cocycles for characteristic classes.
Keywords
Cite
@article{arxiv.1312.1495,
title = {Equivariant measurable liftings},
author = {Nicolas Monod},
journal= {arXiv preprint arXiv:1312.1495},
year = {2014}
}
Comments
Removed the sigma-compactness assumption from Theorem A; minor corrections