Before revision:  We provide a variety of finiteness and continuity results for general risk measures , as well as dual representations for the convex case. We apply our results to risk measures based on Value-at-Risk and Tail Value-at-Risk on L^p spaces, as well as to shortfall risk measures based on utility functions on Orlicz spaces.
After revision:  We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on Value-at-Risk and Tail Value-at-Risk on L^p spaces, as well as to shortfall risk measures based on utility functions on Orlicz spaces.