Before revision:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of Rasonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general  setting.
After revision:  We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of R\`asonyi (2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting.