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On the Distribution Behaviour of Sequences
Author(s) -
Winkler Reinhard
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211860118
Subject(s) - mathematics , sequence (biology) , hausdorff space , countable set , limit (mathematics) , compact space , limit of a sequence , closed set , limit point , space (punctuation) , locally compact space , distribution (mathematics) , second countable space , pure mathematics , set (abstract data type) , baire space , nowhere dense set , borel set , polish space , borel measure , discrete mathematics , mathematical analysis , probability measure , linguistics , philosophy , genetics , computer science , separable space , biology , programming language
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.