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Hausdorff dimension for level sets of upper and lower limits of generalized averages of binary digits
Author(s) -
Cardone G.,
Corbo Esposito A.,
Faella L.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.764
Subject(s) - mathematics , hausdorff dimension , toeplitz matrix , dimension (graph theory) , binary number , packing dimension , class (philosophy) , hausdorff space , hausdorff measure , combinatorics , upper and lower bounds , pure mathematics , discrete mathematics , minkowski–bouligand dimension , mathematical analysis , arithmetic , fractal , fractal dimension , artificial intelligence , computer science
The problem of averaging of binary digits of numbers in [0, 1] is considered. A class ℳ of Toeplitz matrices regular with respect to usual (Cesaro) averages is characterized. The Hausdorff dimension of the level sets of the upper and lower limits of some generalized averages is explicitly computed and it is proved to be equal for every T in ℳ. A description of sets on which finite measures on [0, 1] are concentrated is given using Toeplitz matrices in ℳ. Copyright © 2006 John Wiley & Sons, Ltd.