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1994 | 144 | 1 | 89-94
Tytuł artykułu

The prevalence of permutations with infinite cycles

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EN
Abstrakty
EN
A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category, "almost all" permutations have only finite cycles. In contrast, we show that, in terms of prevalence, "almost all" permutations have infinitely many infinite cycles and only finitely many finite cycles; this set of permutations comprises countably many conjugacy classes, each of which is non-shy.
Słowa kluczowe
Rocznik
Tom
144
Numer
1
Strony
89-94
Opis fizyczny
Daty
wydano
1993-04-04
Twórcy
  • Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395, U.S.A.
Bibliografia
  • [1] J. P. R. Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255-260.
  • [2] R. Dougherty, Examples of non-shy sets, this volume, 73-88.
  • [3] B. R. Hunt, The prevalence of continuous nowhere differentiable functions, to appear.
  • [4] B. R. Hunt, T. Sauer, and J. A. Yorke, Prevalence: a translation-invariant "almost every" on infinite-dimensional spaces, Bull. Amer. Math. Soc. 27 (1992), 217-238.
  • [5] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience Publ., New York, 1955.
  • [6] J. Mycielski, Some unsolved problems on the prevalence of ergodicity, instability and algebraic independence, Ulam Quart. 1 (3) (1992), 30-37.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv144i1p89bwm
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