32 unit (Lower Income) in up and coming neighborhood

[Nate Culkin]

I am looking at a 32 unit right now in Milwaukee, the buildings (there are 3) and units are older, but the place could be spruced up a bit.  It is right on the edge of a neighborhood that is up and coming, median incomes are on the rise, and it seems that the demographics for the surrounding single family homes are beginning to change for the better.  However the apartment complex is in kind of a bubble - its surrounded by a school, police station, and social security office, and is right next to another lower-income apartment complex.  What we are trying to determine is if the surrounding neighborhood continues to improve, how much will this impact (i.e. rents, and the kind of tenant living there) the 32 unit we are looking at.

My question is: has anyone had experience with a lower income multi-family building that had its tenants improve over time as the surrounding neighborhood did as well?  Or do these types of complexes stay 'stuck' as the surrounding area changes?