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Cantor sets and numbers with restricted partial quotients |
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| Authors: | S. Astels |
| Affiliation: | Department of Pure Mathematics, The University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
| Abstract: | For  let  be a Cantor set constructed from the interval  , and let  . We derive conditions under which
When these conditions do not hold, we derive a lower bound for the Hausdorff dimension of the above sum and product. We use these results to make corresponding statements about the sum and product of sets |
| Keywords: | Continued fractions Cantor sets sums of sets Hausdorff dimension |
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, where 
is a set of positive integers and 
is the set of real numbers 
such that all partial quotients of 
, except possibly the first, are members of 
.