While this may be common to many cities, since I live in Portland, Oregon, this is the only place that I have observed this happening.
The bohemian district...the district of art galleries, second hand shops, restaraunts, coffee shops and record stores keeps on moving around, a victim of its own success.
Before I was a part of these things, because I was a child, one of the largest low rent districts in Portland was in Inner Northwest, close to the warehouses and such things. Of course, now this area is known as Trendy Third, with suburbanites flocking their during the weekend and after work to drink coffee at Starbucks and shop at high price botiques. About seven years ago, SE Hawthorne Blvd became the place to be for the culturally minded, although quite a few of those culturally minded were nothing but dirty hippies looking for old Grateful Dead records and shake weed. (At the age of 14, I actually aspired to being one of those dirty hippies.) Now, although Hawthorne still posseses a corner where you can find three head shops in a 2 or 3 block radius, they are all overpriced head shops, and all of the vegetarian restaraunts and bars are also high priced. In other words, Hawthorne has become the place to get high priced trinkets with a left wing slant. At the present time, the place to be for the hip is shifting to Northeast Alberta, a neighborhood that was once Portland's "ghetto", or what passed for it in Portland. Now, what used to be a depressed neighborhood is being ruined by the opening of health food restaraunts and art galleries. Where will it all end?
The way that this happened is all the same: once the down and out folks find a place to hang, the rich folks who think they are still hip all flock there slumming, attracted by the rich cultural life. However, they want their culture a little less raw, in the form of Pottery Barn and Urban Outfitters. Soon, the poor can't afford their old neighborhood and the hip don't want to be seen there, so they have to find some other poor, out of the way neighborhood to spruce up.
And, while gentrification is hardly a new thing, only in Portland does it happen so rapidly, that I know of.