Equivariant measurable liftings

Nicolas Monod¹

¹ EPFL 1015 Lausanne, Switzerland

Fundamenta Mathematicae, Tome 230 (2015) no. 2, pp. 149-165

Résumé

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 $L^\infty $-cocycles for characteristic classes.

Détail

DOI : 10.4064/fm230-2-2

Keywords: discuss equivariance linear liftings measurable functions existence established transformation group acts amenably bius group projective line since general proof simple explicit provide much explicit lifting semisimple lie groups acting their furstenberg boundary using unrestricted fatou convergence setting relevant infty cocycles characteristic classes