Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series

被引：0

作者：

Baranovs'kyi O.M. ^{[1
,2
]}

Prats'ovytyi M.V. ^{[1
,2
]}

Torbin H.M. ^{[1
,2
,3
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

[2] National Pedagogic University, Kyiv

[3] Institut für Angewandte Mathematik, Universität Bonn

来源：

Ukrainian Mathematical Journal | 2007年 / 59卷 / 9期

关键词：

Real Number; Lebesgue Measure; Continue Fraction; Irrational Number; Positive Lebesgue Measure;

D O I：

10.1007/s11253-007-0088-y

中图分类号：

学科分类号：

摘要：

We study topological and metric properties of the set c[o-1, {Vn}] = {x: x = ∑n {(-1)n - 1} g 1 (g1 + g2) \ldots (g1 + g 2 + \ldots + gn)}}, gk ∈ Vk ⊂ ℕ} with certain conditions on the sequence of sets {V n }. In particular, we establish conditions under which the Lebesgue measure of this set is (a) zero and (b) positive. We compare the results obtained with the corresponding results for continued fractions and discuss their possible applications to probability theory. © 2007 Springer Science+Business Media, Inc.

引用

页码：1281 / 1299

页数：18

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