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THE HAUSDORFF DIMENSION OF LAMBDA-EXPANSIONS WITH DELETED DIGITS
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UNSPECIFIED (1995) THE HAUSDORFF DIMENSION OF LAMBDA-EXPANSIONS WITH DELETED DIGITS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 347 (3). pp. 967-983. ISSN 0002-9947.
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Abstract
In this article we examine the continuity of the Hausdorff dimension of the one parameter family of Canter sets Lambda(lambda) = {Sigma(k=1)(infinity)i(k) lambda(k) : i(k) is an element of S}, where S subset of (0, 1, ...,(n - 1)). In particular, we show that for almost all (Lebesgue) lambda is an element of [1/n, 1/l] we have that dim(H)(Lambda(lambda)) = log l/-log lambda where l = Card(S). In contrast, we show that under appropriate conditions on S we have that;for a dense set of lambda is an element of [1/n, 1/l] we have dim(H)(Lambda(lambda)) < log l/-log lambda.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | ||||
Publisher: | AMER MATHEMATICAL SOC | ||||
ISSN: | 0002-9947 | ||||
Official Date: | March 1995 | ||||
Dates: |
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Volume: | 347 | ||||
Number: | 3 | ||||
Number of Pages: | 17 | ||||
Page Range: | pp. 967-983 | ||||
Publication Status: | Published |
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