Lebesgue measure is zero for a set












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In Pollicott and Simon Paper "The Hausdorff dimension of $ lambda-$ expansions with deleted digits https://www.jstor.org/stable/2154881?seq=2#metadata_info_tab_contents he mention that for $ lambda in [1/n,1/l] $, Lebesgue measure of $ Lambda (lambda) $ is zero.
I used Proposition 2 from Keane, Smorodisky and Solomyak paper https://www.jstor.org/stable/2154880?seq=2#metadata_info_tab_contents, for $ lambda < 1/l quad $ is straight forward but for $ lambda = 1/l $, we required that $ l in S $ and that is not mention anywhere in Pollicott and Simon paper.










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    In Pollicott and Simon Paper "The Hausdorff dimension of $ lambda-$ expansions with deleted digits https://www.jstor.org/stable/2154881?seq=2#metadata_info_tab_contents he mention that for $ lambda in [1/n,1/l] $, Lebesgue measure of $ Lambda (lambda) $ is zero.
    I used Proposition 2 from Keane, Smorodisky and Solomyak paper https://www.jstor.org/stable/2154880?seq=2#metadata_info_tab_contents, for $ lambda < 1/l quad $ is straight forward but for $ lambda = 1/l $, we required that $ l in S $ and that is not mention anywhere in Pollicott and Simon paper.










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      -1












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      -1







      In Pollicott and Simon Paper "The Hausdorff dimension of $ lambda-$ expansions with deleted digits https://www.jstor.org/stable/2154881?seq=2#metadata_info_tab_contents he mention that for $ lambda in [1/n,1/l] $, Lebesgue measure of $ Lambda (lambda) $ is zero.
      I used Proposition 2 from Keane, Smorodisky and Solomyak paper https://www.jstor.org/stable/2154880?seq=2#metadata_info_tab_contents, for $ lambda < 1/l quad $ is straight forward but for $ lambda = 1/l $, we required that $ l in S $ and that is not mention anywhere in Pollicott and Simon paper.










      share|cite|improve this question















      In Pollicott and Simon Paper "The Hausdorff dimension of $ lambda-$ expansions with deleted digits https://www.jstor.org/stable/2154881?seq=2#metadata_info_tab_contents he mention that for $ lambda in [1/n,1/l] $, Lebesgue measure of $ Lambda (lambda) $ is zero.
      I used Proposition 2 from Keane, Smorodisky and Solomyak paper https://www.jstor.org/stable/2154880?seq=2#metadata_info_tab_contents, for $ lambda < 1/l quad $ is straight forward but for $ lambda = 1/l $, we required that $ l in S $ and that is not mention anywhere in Pollicott and Simon paper.







      lebesgue-measure number-systems






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      edited Jan 4 at 6:17









      max_zorn

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      3,29361328










      asked Jan 4 at 5:19









      Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao

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