ON THE DISTRIBUTION BEHAVIOR OF SEQUENCES

This paper presents results concerning those sets of finite Borel meas ures mu on a locally compact Hausdorff space X with countable topologi cal base which can be represented as the set of Limit distributions of some sequence. They are characterized by being nonempty, closed, conn ected and containing only measures mu with mu(X) = 1 (if X is compact) or 0 less than or equal to mu(X) less than or equal to 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 g iven 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 possib le measures of this kind. This gives new aspects for the recent theory of maldistributed sequences.