Equivariant measurable liftings
Tom 230 / 2015
Fundamenta Mathematicae 230 (2015), 149-165
MSC: Primary 46G15; Secondary 28A51, 43A07.
DOI: 10.4064/fm230-2-2
Streszczenie
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.
