| Abstract: | This paper presents results concerning those sets of finite Borel measures μ on a locally compact Hausdorff space X with countable topological base which can be represented as the set of limit distributions of some sequence. They arc characterized by being nonanpty, closed, connected and containing only measures μ with μ(X) = 1 (if X is compact) or 0 ≤ μ(X) ≤ 1 (if X is not compact). Any set with this properties can be obtained as the set of limit distributions of a sequence even by rearranging an arbitrarily given sequence which is dense in the sense that the set of accumulation points is the whole space X. The typical case (in the sense of Baire categories) is that a sequence takes as limit distributions all possible measures of this kind. This gives new aspects for the recent theory of maldistribukd sequences. |
