Monod, Nicolas2015-09-282015-09-282015-09-28201510.4064/fm230-2-2https://infoscience.epfl.ch/handle/20.500.14299/119156WOS:000356043500002We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Mobius 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-infinity-cocycles for characteristic classes.liftingamenable actionFatou theoremtext::journal::journal article::research article