The set-theoretic evidence is that we could probably safely add axioms to make many more sets measurable. For example, we could add axioms that would make projective sets measurable.
I'm curious what would be the implications for working analysts of such a move. I can see two potential ways in which it could potentially have an impact:
- Currently, proving measurability of sets is a somewhat fussy activity. With the additional freedom provided by extra constructions, the existing theory would become much simpler.
- There are existing theories that are already straining at the limits of what can proved measurable in ZFC. These theories could be usefully extended.
I could also see that it potentially having no real impact. I'd be curious to hear which if any of these possibilities actually holds.