Colonizing the Moons

Logistics aside, would it really be possible to colonize the moons of the gas giants?

It's my understanding that planets tend to have radiation belts around them.  Would the massive radiation from a planet like Jupiter make it impossible to live on its moons or are some of them outside this belt?  Or could people just live in protected domes of some sort?

you could possible make a dome that protects from radiation by passing a huge current through it and using the flux to stop radiation...it would be ALOT more efficient than simply making a huge dome of lead.