Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 3

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Examples of non-shy sets

100%
Dougherty R.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 1
73-88
EN
Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term "shyness" for this property, and "prevalence" for the complementary property. In the present paper, we construct a number of examples of non-shy Borel sets in various groups, and thereby answer several questions of Christensen and Mycielski. The main results are: in many (most?) non-locally-compact Polish groups, the ideal of shy sets does not satisfy the countable chain condition (i.e., there exist uncountably many disjoint non-shy Borel sets); in function spaces $C(^ω 2,G)$ where G is an abelian Polish group, the set of functions f which are highly non-injective is non-shy, and even prevalent if G is locally compact.
2
Content available remote

The prevalence of permutations with infinite cycles

63%
Dougherty R., Mycielski J.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 1
89-94
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.
3
Content available remote

Which Bernoulli measures are good measures?

51%
Akin E., Dougherty R., Mauldin R., Yingst A.
Colloquium Mathematicum
|
2008
|
tom 110
|
nr 2
243-291
EN
For measures on a Cantor space, the demand that the measure be "good" is a useful homogeneity condition. We examine the question of when a Bernoulli measure on the sequence space for an alphabet of size n is good. Complete answers are given for the n = 2 cases and the rational cases. Partial results are obtained for the general cases.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.