Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T00:47:22.533Z Has data issue: false hasContentIssue false
  • English
  • Français

A set of infinite measure whose ratio set does not contain a given sequence

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

J. A. Haight
J. A. Haight
Affiliation:
Department of Mathematics, University College, London
Get access

Extract

Let G be any enumerable subset of the positive real numbers, with infinity as its only limit point. The purpose of this paper is to give a construction for a Lebesgue measurable set E ⊂ R+, with the following properties:

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 195 - 201
Copyright
Copyright © University College London 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Davenport, H. and Erdős, P.. “A theorem on uniform distribution”, Publ. Math. Inst. Hung. Acad. A, 8 (1963), 3–11.Google Scholar
2.Haight, J. A.. “A linear set of infinite measure with no two points having integral ratio”, Mathematika, 17 (1970), 133–138.CrossRefGoogle Scholar
3.Kingman, J. F. C.. “Ergodic properties of continuous-time Markov Processes and their discrete skeletons”, Proc. London Math. Soc, 13 (1963), 593–604.CrossRefGoogle Scholar
4.Lekkerkerker, C. G.. “Lattice points in unbounded point sets”, Indag. Math., 20 (1958), 197–205.CrossRefGoogle Scholar
5.Schmidt, W. M.. “Disproof of some conjectures on diophantine approximations”, Studia Scient. Math. Hung., 4 (1969), 137–144.Google Scholar