Continuity and measurability of multiplier and projective representations

AbstractIt is shown that various kinds of measurability of a multiplier representation of a locally compact group are equivalent, and are equivalent to the continuity of an ordinary representation of a related group. A unitary representation with measurable coefficients is the sum of a strongly continuous representation and a representation all of whose coefficients are locally null functions. Similar results are obtained for projective unitary representations. This work is carried out without any separability assumptions