The house we live in now had great dane dogs and an invisable fence.  The owners often got tickets for dogs at large, they just ignored the invisable fence.

Problem was, the dogs need to be trained to the fence.  A neighbor put in an invisable fence, and while I passed by his house, i often saw him with the dog on a leash.  As the dog got close to the fence, the owner would tell him to stop, and then let him get shocked.  He did this for at least a week.  After that, the dog would rush out to chase my truck everytime I went by. He would reach the invisable fence, and come to an abrupt halt.  I never saw that dog cross the invisable fence for many years.

Then again, all dogs are different.  Someone once told me to train a dog, you had to be smarter than the dog.  I figure I have not found a dog dumb enough for me to train.