Zero-infinity laws in Diophantine approximation

Y. Bugeaud; M.M. Dodson; S. Kristensen

Zero-infinity laws in Diophantine approximation

Y. Bugeaud, M.M. Dodson, S. Kristensen

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does not have full Lebesgue measure with an the closure of an open set of positive measure cannot be positive and finite. Analogues for $p$-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.

Original language	English
Journal	Quarterly Journal of Mathematics
Volume	56
Issue	3
Pages (from-to)	311-320
Number of pages	10
ISSN	0033-5606
Publication status	Published - 2005

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title = "Zero-infinity laws in Diophantine approximation",

abstract = "It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does not have full Lebesgue measure with an the closure of an open set of positive measure cannot be positive and finite. Analogues for $p$-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.",

author = "Y. Bugeaud and M.M. Dodson and S. Kristensen",

year = "2005",

language = "English",

volume = "56",

pages = "311--320",

journal = "Quarterly Journal of Mathematics",

issn = "0033-5606",

publisher = "Oxford University Press",

number = "3",

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T1 - Zero-infinity laws in Diophantine approximation

AU - Bugeaud, Y.

AU - Dodson, M.M.

AU - Kristensen, S.

PY - 2005

Y1 - 2005

N2 - It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does not have full Lebesgue measure with an the closure of an open set of positive measure cannot be positive and finite. Analogues for $p$-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.

AB - It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does not have full Lebesgue measure with an the closure of an open set of positive measure cannot be positive and finite. Analogues for $p$-adic fields and fields of formal power series over a finite field are established. The results are applied to some problems in metric Diophantine approximation.

M3 - Journal article

SN - 0033-5606

VL - 56

SP - 311

EP - 320

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 3

ER -

Zero-infinity laws in Diophantine approximation

Abstract

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