Distribution functions of ratio sequences, IV

In this paper we continue our study of distribution functions g ( x ) of the sequence of blocks , n = 1, 2, …, where x n is an increasing sequence of positive integers. Applying a special algorithm we find a lower bound of g ( x ) also for x n with lower asymptotic density = 0. This extends the lowe...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2013-03, Vol.66 (1), p.1-22
Main Authors: Baláž, Vladimir, Mišík, Ladislav, Strauch, Oto, Tóth, János T.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper we continue our study of distribution functions g ( x ) of the sequence of blocks , n = 1, 2, …, where x n is an increasing sequence of positive integers. Applying a special algorithm we find a lower bound of g ( x ) also for x n with lower asymptotic density = 0. This extends the lower bound of g ( x ) for x n with > 0 found in the previous part III. We also prove that for an arbitrary real sequence y n ∈ [0, 1] there exists an increasing sequence xn of positive integers such that any distribution function of y n is also a distribution function of X n .
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-013-4116-4