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### Bibtex

@article{40259ef0a9d011dabee902004c4f4f50,

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",

}

### RIS

TY - JOUR

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

VL - 56

SP - 311

EP - 320

JO - Quarterly Journal of Mathematics

T2 - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 3

ER -