Why can't all subsets of sample space be considered as events? My textbook is Probability and random processes by Grimmett & Stirzaker and the first chapter does not explain this," for reasons beyond the scope of the book". The authors introduce the reader to sample spaces and to events and then go on to say that events are subsets of sample space. Then they ask, "Need all subsets of sample space be events ?" and then they say no. But I don't see why not. Can anyone give mean an intuitive explanation for this?

google vitali sets......you cannot measure all the sets if you assume axiom of choice to be correct...however recently there was a paper which showed that you can measure almost all sets if you do not assume axiom of choice
