Several times I’ve heard a theory that goes like this:
If you take all the people in a specific geographical area and divide all their money equally, after a few years everyone will end up with the same amount of money they had before the split.
Is there any evidence to support this?
Is there any “real” information about this or is it just an urban legend?
I would call it an example of wishfull thinking by worshipers of Adam Smith. Don’t you worry about the distribution of wealth, its just as it should be 
I think this fascinating article doesn’t quite answer the question but does address the underlying philosophy.
At least, I don’t think so. Having capital enough to impliment your ideas is a big part of becoming rich. That’s why those investment folks (whaddya call 'em?)
are able to get even richer off the work of others.
It’s entirely possible that someone would be good at inventing, but lousy at raising money. If handed the needed capital s/he could be very successful.
Some folks come by their riches by inheritance, lottery, or just plain luck.
How large a population you’re looking at would be a factor too, I think
Peace,
mangeorge