We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to -cocycles for characteristic classes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-2,
author = {Nicolas Monod},
title = {Equivariant measurable liftings},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {149-165},
zbl = {1335.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-2}
}
Nicolas Monod. Equivariant measurable liftings. Fundamenta Mathematicae, Tome 228 (2015) pp. 149-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-2/